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Actually, the coolest Quickie would be one using the old thoriated globe triodes, which ran on dry cells - like the UV201A. Those things light up a room! How to get 5V .25A supplies to the filaments might be a bit of challenge.....
The way to go here is a type 31 or 71A - that can get the plate impedance down to a more acceptable value so it can drive more than a few inches of cable capacitance. The 31 can use a SLA D-cell (don't know how you'd charge it but there must be a way), while the 71A was originally used with a 6-v lead acid battery, with a rheostat and meter to adjust the filament voltage. You could probably use a 6-v lantern battery. That's getting complicated, but it's probably the better tube. :^)