Hello Big Bill,
I think that a beam power tube may work in this circuit, if you treat it as a tetrode. Beam power tubes are a bit different from true pentodes, so you may be able to get away with this:
Just treat it as if it has two grids and ignore the internally connected third element. The cathode will need to be connected to one side of the heater, probably the side which goes through the rheostat to the common or '0v' connection. Of course, the 1625 uses 12v on the heater. You may need to increase the B+ voltage above 12v. Below is another example:
Imagine that the connection at pin 7 above is the cathode. Again, while the 1625's heater voltage is 12v, 12v may or may not work on the plate. Experiment to find out what voltage seems to work best for you. I have a 1625 available to play with, but I don't think I have a matching socket around now to experiment with.
The idea is to experiment, and have fun! That's how we all learn.