My wife shoots the heck out of my 270 WSM, I usually swap the barrel on her to a worn out but accurate barrel so she doesn't toast my good barrels when she slaps and racks it
I run the 110 TTSX out at just under 3600fps with R17, recoil is mild but I use it for my coyote load and haven't put it on anything bigger. My rifle is braked and is a powder puff to shoot even with full round house Retumbo loads with the 165 Matrix. I think the 130 TTSX would work good and pack a little more steam than the 110gr, the 110TTSX would worry me a bit on an elk just by the way they blow up on a coyote they may be a little aggressive to early.
I set up a 270 Win for my buddies wife and I load it with 140 Bergers right at 3000fps, recoil reducer in the stock and mushy recoil pad. She'll smoke elk and deer right out from under him if she beats him.
The WSM has more snort but your loading it way down to shoot any bullet at 3000fps but the 270 Win may be in a better load range at that velocity your looking for. But then again if you can shoot it later with the 165 Matrix and put the serious smack down on and elk.