Len, how about you build a DC supply, well 2, that you disconnect when you are ready to listen. You get the warm up without burning battery hours and the magic of pure DC when listening.
Great idea!
The Quickie has a DPDT switch for the filament power. It should be easy enough to wire it so it switches between a charger and the tube - so the battery (cell actually) is charging when it's not running. Get a couple NiCd or NIMH D-cells and you're in business. The charging current can be very small - even if you listen 4 or 5 hours a day, 25mA per cell will replenish the charge. You can use the common ground, the cathode resistor just helps comreol the charging current. Add a resistor for each cell and use any old DC supply/wallwart you have laying around.
Here's a schematic (I think what I am actually using; I hope it's not an early version) of the charger I'm using for my 26 output stage. I cut off the 117VAC to the primaries of the charging transformers when the pre is running, so as to avoid any interference. I guess I would figure out a similar scheme for the Quickie.
I noticed when building the Quickie that the HT is indeed switched. That would help in running some idle voltage through the filaments for a "standby mode". IIRC, it should be about 2/3 of the full 1.5V.