You get a reduction from 40 to 35 hours because of your rotary experience (61.109.k.3)
This paragraph reduces the required experience from 40 to 35 hours for graduates of approved programs for an initial certificate. The OP "only" requires the items in 61.109 that specifically say "single engine airplane."
Although training from non-FAA instructors and in non-FAA aircraft "counts," I'm not sure (and am now curious) if a non-FAA instructor can complete the paperwork for the check ride. No written is required, but there is still an oral portion to the check ride. Do you want to prepare for that w/ a non-FAA instructor?
You can also do a commercial add-on instead of private. That's more expensive than just doing the private, but cheaper than doing a private and then a commercial add-on.