Hi Frederick,
I am still struggling to replicate your rather lovely design.  I created a ring region as you suggested:
ringRegion = 
 TransformedRegion[
  TransformedRegion[ringregion, RotationTransform[Pi/2, {1, 0, 0}]], 
  TranslationTransform[{0, 0, 0.5}]]
and then RegionUnion should mesh the two stl images together:
union = RegionUnion[heartRegion, ringRegion]
But, in fact, in Mathematica V12.3, the output appears to be identical to the original heartRegion.
Any idea what the issue could be?