I couldn't sleep so I decided to see if there were any easy DIY solutions. There were many:
At the core of these fixes is putting in a spacer tube to prevent downward motion once the hydraulic cylinder gives up. This makes the chair one height only (or higher), but no one else sits in these chairs, so who cares?
The second one requires less work. I may have some acetal tubing in my spare scraps collection that will do the job. (It is 14o outside; the garage is probably not much higher. I'll wait for morning.) The first requires some chair disassembly to put the tube around the hydraulic cylinder. I will use aluminum tubing to do this fix.
This one shows how to replace the hydraulic cylinder making it as good as new: