Unless you see something, or get adventurous, you're right about needing a new tank.
But a little encouragement:
If the tank is already shot, there's no harm in attempting to repair the output side. You can't break it any worse than it is now.
You might look to see if you can do any disassembly on the output side, possibly even to the point of unwinding the transducer coil a bit, looking for a break.
It sounds scary, but I did this to repair the B+ winding on a PT inside a old VTVM. Tubes inside lit up, but there was no high voltage to run them. Fortunately, the PT had paper insulation that was taped in place. I removed the tape, and after a couple wraps of paper, I got to the point where the PT leads were soldered to the enamel wires making up the secondary winding. After a few turns removed from the secondary, I found the point where the hair-like wire overheating and burned in half. I used a razor blade to scrape off any varnish insulation on the wire, then carefully wrapped 4-5 turns around the tinned end of the PT lead. Some very quick & careful soldering completed the connection, and the repair passed a continuity test.
Replaced the PT in the VTVM (and swapped the rectifier and filter cap for good measure), and it fired up on the first try.
These things can be repaired, they just require patience, a steady hand, and careful soldering.