The new PSU arrived, and we installed it, and got the same symptoms as before. Even when bypassing all other controller circuitry, there is no evidence that the tube is firing at all. This means the problem lies in the (brand new) power supply, the (newly installed, but purchased last year) tube, or the small amount of wire between them.
We've followed these steps, and I've been corresponding with the manufacturer on how to troubleshoot this further, but my time is pretty limited.
@DerrickA4mag & @hectorh: this means there was likely no problem with the old power supply. I noticed it's now in pieces. I put all the pieces in a bin under the laser cutter. Could you put it back together?
The water chiller had a couple problems resulting from disconnecting/moving it during the laser tube replacement. That has all been repaired.