Yes, your are correct - it is probably the 375 Fl Mag, not the 372 2 1/2".
I should have read your post more closely.

First of all, IF you are trying to put Fired cases into the chamber then
they will almost certainly need to be resized if they haven't

If NEW Factory loaded rounds are being used or reloads that were NOT
reloaded from that gun, they may not have been
rezised for that chamber - especially if it is an odd size.

Alternatively, they may be 375 Fl Mag rounds with 375 bullets in them
and not 366 which would also cause this problem.

I would suggest Full Length resize a couple of cases, try these and then
seat a bullet until they also go in.

By the way, I have seen a few like this rechamber and the 375 2 1/2/360
on old 400/360's that had good bores but bad chambers.
Some were good guns if you didn't mind a Wildcat double !!!

Hope this helps.

500 Nitro