Great news: I had a brain storm!
I remembered that my brother is building me a new o-scope built from parts of an old B&K, so it dawned on me that the chassis he built (which is just a power supply at the moment) could possibly power the 7JP4. The scope has a 5DEP1 electrostatic tube, which runs a 2kv anode. We soldered wires to the 7JP4 and ran them to the socket on the scope chassis- it worked! We were able to get a nice bright white spot, even though the anode voltage is a lot lower than the 7JP4 requires. I am now confident the tube I have will at least show a picture, so I'm ordering caps for the chassis right away. Still need a new socket for the tube, though.