I don't have much to add on your PS wakeup issue, except to echo your thoughts around temperature extremes potentially being problematic. Might be worth doing a close inspection of the joints in the PS control circuitry. There are detailed service manuals available for the 11301/11302 on the TekWiki site that may detail some similarities to the DSA power supply, which may help your efforts. The DSA power supplies do contain the dreaded RIFA caps, and I have one PS that now has low rail voltages as a result of a RIFA failure. You might proactively replace these if you have not already.
On your 11A72 errors, I recently had a spate of calibration errors in my 11A34 amplifiers (gain and step gain typically), that ultimately got corrected by a good cleaning and torquing of the Hypcon connectors that hold the M377 chips in place and provide contact from the ceramic substrate to the etched circuit board. My DSA is not in the best thermal environment, and I suspect that the temperature cycling may have had something to do with the 11A34 problems I had, but I don't have proof.
What I did learn was a casual cleaning of the Hypcon connector simply will not do. My first couple of attempts using IPA and a fine, medium stiffness art brush was ineffective. After several attempts at cleaning this way, I thought surely there couldn't be an issue remaining with the Hypcons, But the problems remained and the symptoms kept pointing to an issue with the M377s. At one point I had concluded that one of the M377 chips must be failed, and received a humorously curt congratulations from John Addis on having the only M377 known to him to have failed! So, not wanting that distinction, as a last resort and as suggested in the manual, I firmly, but carefully, scrubbed the traces on the M377 hybrids, the embedded connector leaves in the Hypcon and the corresponding traces on the ECB with a white Stadler-Mars drafting eraser. Followed by canned air (another topic),brushing with aforementioned brush (no IPA), and close inspection under magnification for any remaining detritus. Problem solved after a couple of passes through EA. Lastly, these connectors have a torque spec. The best I could do with that was to try to evenly torque, by feel, at what I thought was a reasonable torque.
Your 11A72 doesn't have the M377 preamps, but it does make use of Hypcon connectors on the input and output amps if I remember correctly, so if your amplifier errors return, you may want to try a cleaning. Like you, I'd be suspicious the PS and amp errors could be related, especially if the amp error clears with a "good" PS startup. I felt the same way about my multiple 11A34 amp failures, and at first I thought I had a mainframe issue, but in the end it was "random" multiple failure in the plugins.
Good luck, and hope to hear back on the PS wakeup problem. It will be good to have that documented.