With RunGap there is at least one option for @xterrastrial assuming TR is already syncing to Strava.
Once in Strava, RunGap can pull the workout and push it to Apple Health with HR data.
Strava ← RunGap → Apple Health
RunGap can sync with a LOT of platforms, but currently does not support TR so you need to use something like Strava as intermediary.
RunGap doesn’t constantly check, sometimes I get impatient and open RunGap, let it sync, then wait for Health on the iPhone to sync to my Watch. Once that happens I get full Move and Stand and Exercise credit just as if it was recorded on the watch. 