Welcome to the 350 RM club, the COL limitations in all the remingtons is similar 2.8" that includes the 700 Classic that also came in 350 RM.
I use a 350 and have not found a problem using 200 gr Hornady and 225 Partitions, using 250's will crowd thing a bit but new powders have hit the market that might give you a little more breathing room. I assume your problem is the 250's, try to use spitzers instead of boat tails since they are usually shorter than the same weight in BT's. A compromise would be something like the 225 Sierra SBT. For deer hunting the 200 Hornady SPTZ has been the cats meow for me, I have only recovered one bullet in all the deer I have taken and only because the bullet split in two and the jacket stayed in the animal.
The Model 7 has two advatages over the 600/660 and that is that it has a drop floorplate and a regular bolt handle but aside from that they are similar.
Good Luck
BB