I also have a great eater who will usually only eat the second time around. I let her strike, constrict, then I just go off and get some pretty much boiling steaming water ready. I swipe her mouse just as she looses interest, warm it up for 30 sec, and dangle it...she always constricts for s shorter time the second time and then eats it.
I think she just spends so long constricting that the mouse cools down too much to be edible.