I've done this more than once.
No you don't have to remove the rear head, however you need to be sure you've removed and disconnected everything. Not all bolts go through the engine some just mount into the heads. I can't remember exactly how many there are, 6 probably.
Assuming all bolts are out is there any movement in the engine, you should be able to rock the engine? If not the engine mounting adjusters might be holding the engine into the frame. They are castellated nuts and can be a little stubborn on occasion.
If you have got movement check the rear exhaust pipe. If you still have the stub on the head it can catch on the back of the frame and prevent removal. As you take the engine out you need to move it forward slightly as it drops down.
Other than that without seeing what you have removed it will be difficult to suggest what is presenting the challenge.
Turning to the what to do with the engine question, the most common answer is a
Cam Swap. Other than that, how much do you want to spend? Big bore, lighten flywheel, Hayabusa pistons, thinner head gasket, the list can go on. If you have cams to hand chuck them in. If not check the valve clearances and shove it in.