Solved!
"Eppur, si move!"
OK, after much nail-biting, I finally built a test jig as discussed above and powered up my linear actuator. Thanks to the help, support, advice and warnings of Hero999 and iainwhite, the experiment came off without a hitch. No sparks, no smoke, no grinding of gears; just a quiet, steady advance of the cylinder.
Because I know that inductive loads can produce large voltage spikes when powered down, I ramped up the voltage slowly on the variac, advanced the tube a few centimeters, then gradually reduced the voltage back to zero. Don't know if that was really necessary, but I believe in being careful. I have not yet bothered to disconnect the crimped-on terminals which connect to the DC output of the rectifier to reverse their polarity, but my guess is that simply swapping these two leads will allow me to power the LA in the opposite direction. Problem solved!
Now, I'm curious about what kind of control circuitry was originally involved. I've seen various "black boxes" that allow a nursing bed to be raised and lowered, but haven't had the chance to tear one apart. And since they cost a bundle, I don't want to buy one. Based on circuits I've seen posted here and elsewhere, what I need is a hefty DC power supply for the motor plus the control circuit itself. This might incorporate an H-bridge, a momentary toggle switch and a power transistor (MOSFET?), and a lower-voltage input to fire the transistor. I will likely also need a snubber circuit incorporating a couple of diodes (one for each direction of current flow) and a resistor. Since I don't yet have any reliable specifications for the motor, designing this circuit is not a big priority right now. But if anybody can point me to an example circuit to get me in the ballpark, that would be most appreciated.
The DTG110-92 is about the size and shape of a 12oz beer can and runs on 110VDC. Absent any test gear, I can't even guess how much current it draws, let alone what the induced voltage spikes might look like, though I guess a DMM set to measure current in series with the load while it's powered up would get me started, right? From there I could presumably calculate power dissipation and start looking through datasheets to find parts that will stand up to use in a such device.
Hmmm, speaking of 12oz beer cans.... Gotta go!