The above hints that the problem lies in the backend.

That's what I originally thought...

The problem looks like the one fixed in Pike 7.7's backend.cmod 1.174:

| revision 1.174
| date: 2005/04/13 14:16:43; author: grubba; state: Exp; lines: +45 -4
| Fixed deadlock in BACKEND_USES_DEVPOLL mode for POLL_DEVICE_SET_EVENTS() hanging when the backend thread is in MY_POLL().
| Fixes performance problems with Roxen on Solaris.

That fix may not have been backported to Pike 7.6.

Actually, I backported that fix a few months ago, which did fix problems with SSL, but it doesn't seem to fix this problem. The main thread does wake up on signals, but none of the handler threads will break out of their read() on the thread queue.