I just purchased a compact crank, Shimano R700, and would prefer a 36-tooth inner ring over the 34. Does a 36-tooth ring exist for the Shimano compact crank, I can't seem to locate one using Google? I have read that a 36 would shift a little easier due to a smaller big-little ring tooth difference.

It wouldn't have to be a Shimano ring. You just need a good quality ring with a 110 BCD pattern. One option would be a TA Specialties ring from https://www.peterwhitecycles.com/chainrings.asp.
Be sure to get a 10-speed model for a Shimano compact crankset.
Al