There were two issues here:
1. Searches for a subset would overlap a found area. So if the search string was R,4,R,4 and the string was R,4,R,4,R,4, it would say there were 2 matches in there since it re-used the middle set.
2. It would happily find a subset that was too long. 20 characters is the maximum program length, per the instructions. Huge thanks to the intcode program for having this as a diagnostic message.
Now this can solve both input sets I have access to.