I am wondering how to deal with other two hole for water.
See my pipes configuration.
I normally use a Moen Posi-Temp with their #1920 remodel plate.
I see you have plenty of room there to work with.
To cut the tile, I use a tile router with tile bit. It cuts the tile like butter.
The trick, is to position the new valve up a little higher to make room between the pie pan and the tub spout.
Instruction Sheet for the 1920 remodel plate