I did the 9V battery thing, at school no less....
They said our project had to be battery powered, so I did a tube guitar amp with 60 9V batteries in series for the plate supply, and 3 2V rechargeable cells for the filaments.
The bias battery was by contrast tame, just two 9V batteries.
Top tip: Insulate the batteries in blocks of 5 or 10, the case to internal doings insulation layer in the battery does not like 540V!
Second top tip: If using nicads, make sure the fuse is good for breaking DC at that voltage, turns out the glass ones get 'splodey.
I was however generally known to be a much better electrosmith then the teacher was, and my stuff generally kept the high tension behind plastic so was at least somewhat safe to use.
Teacher was cool with it, just so long as I didn't bring the battery charger anywhere near the school (Voltage doubler off the mains, with caps chosen to provide the current limiting impedance, but at least it was touchproof with proper connectors).
Regards, Dan.