For the sake of comparison, I also tested with my bench supply.  I was interested in how well the fan worked when supplied as much current as it wanted, and noticed a difference but it was not huge.  The fan pulled about 0.13A @ 12V.  I also used the flyback diode in this set up (again note the diode is not needed and was removed from the final design).

I tested this again using only the battery which was fully charged using the board shown above.  I found that I had to turn the potentiometer down just a touch from where it was when running on the USB input, but it was still able to reliably deliver 10.1V (didn't check the amps this time but the fan seemed to have a good amount of suction). 

I tested the suction using a candle and a toothpick to generate some smoke and was able to hold it about 5" away and get the fumes drawn into the fan. It was usable for about 50 minutes off the fully charged battery (which by then measured 3.41V), and dropped out to being barely on at 53 minutes, at which point the battery was at 3.40V.  I did the test with the carbon filter in place, and so I think this may be the answer to the problems I had previously (larger fan and larger battery).  One issue is that when used upright at least, there seems to be a sweet spot where fumes get sucked through the fan, but outside that area which may be 2" wide, it will start to go around the fan (but still gets sucked away).  I think adding some folding shutters to the sides may help keep more of the fumes going through the fan than around it.  The problem however is that this fan is crammed full of stuff and there is no room to add that (update - the final design incorporates a simple duct to help with this issue).

I also found a way to add a micro mini (low profile) fuse and fuse holder to this without changing much of the design.  The fuse will be accessible from the front and shouldn't look too bad.

The following is the product info for the DYP-ME0010-A smoke sensor relay

Operating voltage: DC9V
Standby current: 10UA
Induced current: less than 30MA
Output: Relay normally open, normally closed, or the output high and low
Sensitivity: Adjustable
Working temperature: -5 -50 ℃

Smoke module wiring instructions
Black: Power ground
Red: positive power supply DC9V
White: Relay normally open
Blue: relay common
Green: The relay normally closed terminal

Simple test method:
1. press the test button 3S, light starts flashing, the relay normally open relay with common terminal connected.
2. can also be smoking cigarettes, the smoke blowing in the maze, so 3S light starts flashing, the relay, the relay is turned often start with common


My Notes:

Adjusting the POT clockwise seems to increase sensitivity (I only went 1/2 turn since it may not have a stop).

When it detects smoke, the LED will flash (prior to triggering), and then when it finally triggers, it will flash continuously for a bit and then slower, which I think is just indicating some threshold is met on the sensor.  When triggered, the relay will switch, but will only stay latched for about 1min before switching back if the smoke is removed.  When triggered there was 8.63v on the "out" line on the header to the right of the relay (that was with 9v input Vcc for the sensor), I suppose that could be used for an alarm or buzzer.

If power is disconnected, the relay it will revert to the normally closed (green wire) terminal connected to common (blue wire).  Interestingly I triggered it, and accidentally pulled the ground wire, which flipped the relay back to NC, but when I reconnected it, the relay went back to NO (alarm) for less than a minute before reverting to NC, possibly due to some residual smoke still in the sensor.

This relay does not latch so it won't be good for keeping something turned off after smoke is detected which sucks.  Will need to use some additional logic or circuit stuff to make that happen.

The circuit diagram is just an outline for what I am hoping to build.  The quality of the pic above sux and I can't seem to fix that since the decent (readable) image I uploaded is getting optimized or something when it is posted.  I have not used the NodeMCU and my Arduino skills are really rusty, but there are enough tutorials out there and libraries that should help with the hardest parts of making this happen.  The following are the major components I plan to use:

• 9V Smoke Detector Relay (Ebay: Smoke Sensor Module Smoke Detector w/ Relay Output J6J4)
• 30A 12V Realy with logic level input (Ebay: 5V/12V/24V 30A Optocoupler Isolation Relay Board Module High/Low Trigger)
• NodeMCU (ESP8266)

The first part of the project was to set up a battery backup circuit.  I wanted to have it run from a 9v battery in the event that mains power was down.  So I found some examples of exactly what I was looking for, and used them.  The P-Channel MOSFET is apparently ideal for this task since it normally will conduct when the gate is at 0v (assuming that the Source voltage is positive).  Below are the links to the info I used  or found helpful for the battery backup part of the design so far:

Good explainations of P-channel MOSFETS:
https://www.baldengineer.com/p-channel-mosfet-tutorial-with-only-positive-voltages.html
https://www.youtube.com/watch?v=14mYnsWK7QM

Example battery backup circuit designs - the design below is duplicated from these:
https://electronics.stackexchange.com/questions/219353/battery-backup-supply-switch-over-design
https://www.disk91.com/2014/technology/internet-of-things-technology/make-an-usb-power-supply-with-backup-battery/
https://www.eevblog.com/forum/chat/battery-backup-circuit/

Since I have not used P-Channel MOSFETs in the past, the youtube videos saved my sanity when I thought I had screwed up (but hadn't).  I had also read several things online that put me on a wild goose chase for a "depletion" mode P-Channel MOSFET - which are like hens teeth - and not necessary.  For some reason, almost all of the P-Channel MOSFETs available are "enhancement" mode, so the depletion mode type are unavailable or very expensive (in that small quantities are not available).  Anyway enhancement mode work just fine for this it seems, and so once I got back on track with that, I was able to order some and give it a test. 

P-Channel MOSFET notes...

The pics further down show my test setup with the mains power (the voltage regulator on the left) turned on, and a backup 9v battery connected.  The P-channel MOSFET is the "IRF5305PbF" and the pinout is Gate / Drain / Source (looking at the labeled side of the part).  This part has a "Gate Threshold Value" of -2 to -4 volts (that's right negative voltage).  Specifically the Gate Threshold Voltage is the voltage difference between the Gate and Source.  The link above for the baldengineer.com site has a good explanation of what it takes to trigger a P-Channel MOSFET, which I understand (in this case) to be basically this:

Gate Voltage - Source Voltage > Gate Threshold Voltage = OFF

Gate Voltage - Source Voltage <= Gate Threshold Voltage = ON

There may be more to it than that, but that's how I understand it now.  So in my case, the Gate would be 12V and the Source would be connected to my 9V battery.  The drain is connected to the Vcc going to the LED's in this test case.  Therefore, when the mains is connected and there is 12V input to the device, the battery should be disconnected completely (12V - 9V = 3V >  -2V)  where -2V is the higher end of the Gate Threshold Voltage from the datasheet. If mains power is lost then the 12V on the gate will drop to zero and the battery should be allowed to take over (0V - 9V = -9V < -2 (to -4)V) so the P-channel MOSFET should be ON, connecting the 9V battery to the Vcc Supply line for the rest of the circuit.  I tested this and it seems to work well, though I have left in the Schottky diodes to protect from reverse polarity on the battery (they may not be necessary but since I have volts to spare I am leaving them in).  I probably could have used regular diodes for the reverse protection, I just wanted something to protect against an accidental, and brief flipping of the battery connector when installing it, I don't thing there is any point to the diode after the 9v regulator though and probably would remove that from the final design.

So here are some pics showing the testing - first the scenario where mains is on, and I don't want the battery connected at all.  The multimeter is testing current flow from the battery positive to the P-Channel MOSFET source pin (there is a diode in there also).  There is no current because the MOSFET is not conducting.  Note that there is a 9v regulator but the gate is connected to 12v.  The 9v regulator is fed by the 12v supply on the left which is also where I get the 12v for the gate, and the regulator outputs 9v into the power rail that the LED's supply from.

So here the test with the mains power on, supplying 12v to the circuit, and the LEDs (supplied from the 9v regulator) are also on.  The battery is disconnected since the MOSFET is not conducting:

Gate Voltage - Source Voltage > Gate Threshold Voltage = OFF
12 volts   -  9 volts > -2 (to -4) volts  =  OFF

Next is the condition where mains power is down, and the battery must take over.  It is the identical setup as above, I just turned off the 12v supply on the left.  So now the gate voltage is dropped to zero, and the supply (where the 9v battery is connected is still at 9v). Note that the pics don't show the LEDs being on very well since these are color changing LEDs (what I had handy) and they transition so when I got the pic only one appears lit - but they were all on.

Gate Voltage - Source Voltage <= Gate Threshold Voltage = ON
0 volts   -   9 volts   <   -2 (to -4) volts  =  ON

So that's pretty much that for the backup and power part of the circuit.  The rest of it will be the hard part - programming the NodeMCU to do my bidding - and I am not sure if that will kill this project or not.