I have two 350's in a model 7 and model 700. I don't have mag issues and shoot the 200 TTSX no problem.
I have seated and shot the NP 250 and the Swift 280 grain with no problems either.
Curious what your COAL is when loading for the mod 7? I can't fathom how the mouth is not on the ogive for the 200 TTSX. Do you have any pics of loaded rounds for the 200 TTSX, NP 250 and the 280 Swift?
I can't load past 2.80". That said, I have used the 225 Woodleighs because of the RNSP geometry.