The solution I ended up taking solves a few problems at once: how to gently agitate the specimen, and how to keep the specimen fully submerged despite its tendency to float.
Here is the solution:
It uses the focus stacking controller that I built, just with a new mode added that does nothing but turn the motor back and forth, like a washing machine on the agitation cycle.
Since I use hot water + soap solution, there is steam involved that condenses on everything inside the container. To prevent the motor from getting wet, I placed a rubber o-ring between the motor and lid, and used nylon spacers where the screws are, between the motor and lid, to give the o-ring room. I smeared plumber's grease between the shaft and motor to prevent moisture from seeping into the stepper motor body. Finally, I put some vent holes in the lid for steam to escape through.
The specimen is put in a wire mesh tea ball, fully submerged, and the motor attaches to the tea ball using a coupling and some brass wire.
The focus stacking controller needed no hardware changes, just a small addition to the software.
Since I had all of these parts already, cost was $0 and the whole thing probably took 45 minutes to assemble, including writing the code. This doesn't include the prior cost of the parts of course, or the time already invested in building the stacking controller.
Maybe this will inspire someone to a similar end... it's not pretty, but it seems to do the job quite nicely.
