I had a 7mmRM for a bunch of years. Shot a moose and a few deer with it.
The first load I would try if I get another one would be the 162 Hornady BTSP Interlock, that's a reliable standard load that is hard to beat and won't cost much. The next one I would try is the Federal Fusion 150gr, I have had very good luck with every caliber Fusion load I have tried.
A handloaded 162g Hornady InterLock was what I used to take my first big game animal, a 20” spike bull elk. The bullet was launched at 2950-3000fps and impacted at about 110 yards, full broadside. It hit a rib dead center, creating a more or less caliber-sized entry and cratered the back side the full width of the rib. After slipping between the off-side ribs it came to rest under the hide.
That bullets only retained 47.7% of its original weight, even though the challenge to its integrity was not great. The next year I switched to 160g Grand Slam bullets. It took me 20 years to recover one and when I did it had destroyed both shoulder joints on a 5x5 bull. This was also on a broadside at about 110 yards. It was also under the off-side hide when found. The Grand Slam retained over 70% of its original weight even though the challenge to its integrity was pretty severe.
These days I shoot true premiums – North Fork, A-Frame, TTSX and MRX – and don’t worry about bullet performance. I’ve found they work at all ranges near to far (high impact velocity to low velocity) and I’ve launched them at velocities over 3300fps. My 140g North Fork load runs over 3200fps in my 7mm RM. A couple years back I drove one the full length of a forkhorn mule deer. Good luck trying that with a 162g InterLock and short-range (high velocity) impacts.