I wouldn’t worry about doing the exercises in a way where you don’t drop your heel below the level of your toes.
But aye – use the good leg to lift you upon to your tip toes, then lower on the gammy leg. Pain is to be pushed through for once (within reason).
HOWEVER – if you have insertional achilles tendinopathy you need to find a different solution. You’ll need to see a good physio to sort that out.