If I was going to cut up an AE86 and put an engine in that didn't belong the only conversion I would feel confortable with is a rotary. I would NEVER do the Nissan thing but a Mazda rotary I think it would be good choise. When I was working at a workshop here in Brisbane a few years ago we fitted a 13B into a TA22 Celica. If I remeber it turned out really well and was easier than what I would imagine a 20valve conversion would be. It was carbureted and ran a points ignition so that side of things was kept simple. We used a Mazda RX7 5 speed gearbox and the biggest drama was making a gearbox crossmember. As I remember it was great on the road and went really hard.
Cheers