Shut down PC last night. Had a message from Support to try uninstalling the F-15E module, so started the PC back up and logged into DCS (still with "clean" DCS install and "new" ...\saved games folder).
Loading time improved and no random black screens. Tried various "instant action" and "training" sessions. Stable and no issues. Reverted to "old" saved games folder and tested again: no issues.
Looks like the old "switch it off and then back on again" trick worked for me.