After loading the savegame, the game had another minidump. This one also occured when I tried building a starbase, just as it went from migrator to star base under construction. The starbase was not under attack at the time, so that causing it is ruled out. Perhaps some sort of limit on starbases which if exceeded causes a crash? Going to try again under various conditions.
Edit: After loading the savegame again, it seems to be able to build starbases just fine if no enemies are in the gravity well. Going to try some more with enemies in the well now.
Edit 2: Turned down all effects settings to minimum, no effect. Still minidumps when building a starbase in area with hostile fleet.
Edit 3: After further testing, if I send in ships before I send in the migrator, no minidump occurs. My guess would be a problem with the code involving AI targeting the starbase at the moment it goes from migrator to under-construction-starbase.