In my unscientific mind, "hot" would be too hot to touch.
Regarding flyback output, the data sheet for that CRT says the typical anode voltage is 12KV. Recommended max = 14KV, min = 10KV.
http://scottbecker.net/tube/sheets/093/1/16GP4.pdf
That would be measuring at the end of the HV anode lead. Since the CRT lit up before, I'm guessing you have several KV, at least.
I wonder if the 1X2 socket could be faulty? Have you carefully inspected it using a strong light, and looking for any cracks, black carbon trails, etc.? If you leave the doorknob disconnected and use a listening tube, perhaps you could tell whether the Pfffft sound comes from the socket.
Phil Nelson