You’re on the right track. At our program, we basically looked at it in this order:
1) Program (especially for home students that are really liked)
2) ITE scores
3) LORs/Connections
4) Research
In general, ITE scores are much, much less emphasized than Step 1. Also these fields are very compact with a relatively small number of folks involved in national organizations/research (in cardiac, its the same 30 or so that do the lion’s share of the publishing and sit on SCA boards) - a letter from a big name can and does go a LONG way.
Basic exam has no impact whatsoever, assuming you passed as the scaled score is not released to programs as ITE is.
SF Match also asks for AKT scores, but the number of programs that still take it continue to decrease so we basically threw it out. That being said, it shouldn’t be surprising that high scorers do so throughout their standardized tests