First, I don't shoot a 7 Mag, I hope that doesn't disqualify me from trying to help.
I do shoot 2 other belted mags. For sizing just bump shoulder .001" or .002".
How are you cleaning the barrel and what are you using to clean it with?
Personally, I like Boretech products.
I've noticed in "production" hunting rifles, even "lapped" barrels, a tendency to copper foul a little quicker. Usually drops off after a while, but sometimes it doesn't.
That, and your barrel is relatively new?
Also, I've not switched bullets or powder without a complete down to bare metal cleaning.
Have you taken the rifle apart and inspected stock bed and receiver for any indications of high spots, excessive rub marks, etc?
You may want to try lightly loading the barrel in the stock with a folded business card or two. Note whether groups get worse or better.
Also, when it comes to magnums, especially hunting profile barrels, I like to wait until the barrel completely cools between shots.
If the action or barrel is "loading up" in the stock due to heat, and your groups open up, that may indicate some kind of alignment or pressure issue with your barrel/stock or receiver/stock issue.
The point is, within reason your magnum rifle should shoot the same all cold barrel as it does shooting once every 2-3 minutes.
Magnum rifles with light hunting profile barrels typically don't shoot tight groups one shot after the other.
There really isn't a need for that for their designed use, but if they do it's more of a bonus than a requirement.
You are going to need to get off of the PPU Brass I'm afraid. I don't know who makes quality brass for the 7 Mag, but someone should be able to get you going in the right direction.
If you don't find anything, it may just be a picky rifle and you'll have to keep trying to find what it's going to like.
Hope this helps you out somehow. Good luck with your rifle!