"Would the module throw an error message if its Dallas-chip-battery is gone? "
The 11A34 extended service manual indicates that if the U801 "dallas" chip battery is failing, the plugin will generate a "CKSM Plug" failure. It goes on to note that "In firmware versions of 3.4 or greater, the CKSM Plug diagnostic is not run as a power-up self-test, but is run to decide whether Enhanced Accuracy status has been retained".
I do not know for certain, but I suppose it might be possible that failing the CKSM Plug test request from the mainframe in firmware 3.4, could trigger a partial EA at startup. Your 11A34 is F3.3, so this doesn't seem to be your issue, as it sounds like it would report this as a self test error. I don't think there is extended service info for the 11A33 and 11A72, so uncertain if there is a similar FW difference for those amplifiers.
Have you tried installing only one amp at a time to see if you get the same results of a partial EA at startup (after the initial partial EA due to the reconfiguration)?
Also, as an additional data point, my DSA has FW 2.23, and doesn't have the issue you describe. It has however done a spurious "TekSecure" erase 2 or 3 times in the last 5 years or so.