I shoot a 22-204 which is about like a 222 Rem Mag Improved, slightly more capacity than the 222 RM. The 222 RM is very close to the 223 AI in capacity. Hornady and Lyman have plenty of data for the 222 RM with 40gr bullets. 4198 is a little on the fast side for the 222 RM with heavier bullets but from the data shown should work well with the 40's.
I shoot 40gr NBT's out of my 22-204 for coyotes and have a feeling that full power loads of 40gr HPs in the 222 RM will be a little heavy handed for fox if your trying to save fur, if not saving fur DRT should be the story of the day.
Good luck to you let us know how it works.