There are a few things you can test or replace before the coils. First because the fuses arent blowing immediately upon starting a game, but only after using the flippers the mosfets on the board are probably not shorted on. You can look on pinwiki for how to test with a meter to make sure.

So even though you are showing good resistance at the flippers you could still have a bad winding. To have it on both flippers is fairly unlikely but it could happen. If after testing the mosfets on the board they look ok, change the diodes on the flippers.

Report your findings and we can take it from there.