I finally had time to assemble all of the parts to the water storage system for the water table. I ended up using kegs as water storage containers since they're designed to handle the pressure. The system uses compressed air to force the water up into the table from the kegs.
The good news is that it works well! It fills in a few minutes and drains in about 10 minutes. I'll probably end up welding a bung for the drain to increase the water flow or modify the tap to increase the output diameter. But for now it's functional. And I definitely need to add a baffle on the outputs; the water splashes up when you start & end the filling process.
The bad news is that it only works with the kegs vertical. And unfortunately they are about 1/2" too tall to fit underneath the stand I built. I have two options: 1) cut big holes in the top sheet to fit the tops of the tanks, or 2) raise the whole table about 1". I haven't decided yet which approach to take.
Also, there were a few drops leaking from underneath the 2nd time I filled it. i'll have to check it again to make sure there's no additional pinpoint leaks I missed in my previous tests.
I made a video walking through how it all works: