Alright, I just checked again on my ABSOLUTELY CLEAN INSTALL. After over 15 minutes realtime of waiting, still not getting any form of "Mansfield wants to talk to you" corner-message (the call that I
know will trigger quest "Doctor in the House") with the MCM option for "HQ Radio Auto Contact:" switched to OFF.
(save has a couple of plots built because I was checking corner-messages were working at all and not doing that 'those just stop showing for the rest of this game session for some reason' thing I've never managed to resolve and nobody else ever mentions happening)
Here is a save at that point (running absolute bare minimum load order, no Extended):
Other notes:
Stodge did spawn with his "Stodge's Rags" in his inventory, but they weren't equipped.
Also, quest-skipping past "How to HQ" gives this questlog update (in this specific instance, it should be Sanctuary, not [...]).
(this isn't new, just noticed it again now)