First, IMR 3031 is too fast of a powder to be well suited to the 7mm Rem Mag. Go with the RL-22.
I have used the Winchester WLR with RL-22 and 160g bullets in the 7mm RM with good success. The WLR has a reputation for being the hottest standard rifle primer though, so IMO it's the most suitable replacement for a large rifle mag primer.
I haven't tested this load, but an older Alliant Manual lists:
Remington 9 1/2 Magnum primer
3.275" min OAL
Hornady 139g SP
70.0g RL-22 MAX (So start at 63.0g and work up, watching for pressure signs)
The claimed velocity and pressure in a 24" barrel was 3,295 fps @ 58,000 psi. Starting with the min load, you could swap out the primer with what you have and work up and see how it goes.
Good luck.