The remote has an interesting design, instead of just using low voltage signal level stuff, I found that it actually contains the MOSFETs which would drive the linear actuators. That means the motor current has to go through the remote controller (and remote cord), which is not a problem, just not how I expected they would design it. In any case, this probably makes it easier to troubleshoot, and if the board goes bad, it's just the remote that needs to be replaced (at a cost of about $77).
Fortunately, when I opened the controller (there are 5 screws by the way, with one under the label), I found that one of the wires had broken off (probably from years of slight twisting of the wires, despite the pretty robust strain relief). After cleaning up the wire and the hole it goes into, I found others were also a bit broken, so I removed a total of 4 wires and resoldered them. Then I added a zip tie for strain relief, and covered the wires in hot glue for good measure, so they'd be less likely to break again. Next I cleaned up a decade of crumbs which had gotten into the remote, cleaned the silicone oil that had leached from the number pad, and then cleaned the board pads with alcohol to remove the remaining oil there. After that simple fix, it works like new again. It's not a big deal, but I haven't been able to post much lately and thought the pics may help anyone with a similar remote, or a similar problem with it.