@alexberger Since an SET is a constant current load insofar as the power supply is concerned, it won't make much difference if you use tube or solid state rectification. But you might want to consider what happens when the AC line voltage changes. The filament of a tube rectifier cools off when the AC line goes down- so the B+ voltage drops more than one might expect since the rectifier gets less efficient. . Plus you'll find that they each have a 'sound'. If you set up HEXFRED rectifiers properly they are about as neutral as it gets.
FWIW we run a separate power transformer for the driver section in our OTLs. We did this so as to prevent any modulation in the output section power supply from affecting the driver. This reduces IMD. Our OTLs run class A2 and have dual output section power supplies so modulation of the supply could be a concern.
In an SET a separate power transformer for the driver isn't going to have the same effect since the power supply for the B+ should be nice and quiet anyway. The separate transformer would be useful if you planned to direct couple to the power tube with a cathode follower though.