You know I was always taught as a kid to cut the head off, then split back from between the pelvic fin to the anal fin and gut them. That is the way everyone did it in the piedmont fishing warm water if they weren't big enough to filet. Nowadays, if I'm Crappie fishing or catching a mess of Bream for the pan, I'll usually filet them out with a good knife but when I keep a trout I still go the old method of removing the heads and gutting them. Butterfly them open just as you did and grill them on the gas grill with lemon pepper and melted butter mixed together basting about 2 or 3 times in 10-12 minutes.
I remember when I was about 12 years old I saw some migrant workers eating some fried Bream from the pond and they still had heads and eyes, everything and that was a big suprise to me, I'd never heard of fixing them like that before!! I don't even know if they removed the entrails and I didn't ask!