If you are adjusting your rest to get your broadheads closer to your field tips then you field tips WILL change their point of impact as well. If you cannot get your BHs and FTs to hit at or very close to same POI than you likely do have either a spine issue or fletching contact issue.
Just FYI - I was having the same problem with my PSE DNA. Shooting the same draw weight and draw length and same arrows as my Martin Firecat. I finally resolved this by going to a heavier spined shaft. I can only surmise that PSE shoots a much faster arrow with a more radical cam which required the stiffer arrow.