The good news is: it works.
The bad news is: it needs tweaking to work.
First thing I run into was that the GUI was hideously slow. I would click on a button in the profiler, and feedback would take several minutes. I'm not joking. Several minutes. Googling revealed a Sun Bug Database item "Antialiasing/Compositing is slow on remote display". It suggests that to run GUI Java apps over X.11, one should add
-Dsun.java2d.pmoffscreen=false
as a JVM startup flag. I added it to profiler's yjp.sh launch script, and Holy Moly, it became much better. Granted, it was now rendering screens progressively from top to bottom, but it did it in matter of seconds, not minutes. It now felt like something out of 1999 instead of 1993. Further Googling for various combinations of "X.11" and "slow" and "ssh" turned out sites that suggested it's possible to make x.11 over a bit faster, by telling SSH to use Arcfour or Blowfish ciphers instead of AES, as well as to compress the traffic:
ssh -c arcfour,blowfish-cbc -C -X host
This led to further improvements; the progressive rendering got faster by another factor of two. That's as good as it gets. Now it feels like something out of circa 2001. I can work with that.