Hmmmm
My Speer manual (no 13) shows 300 Win mag w/ 130 gr bullet at 3465 fps with the top velocity load & the 270 Win w/ a 110 gr (sorry no 110 gr) at an even FASTER 3436 fps.
Not sure what the speed has to do with the pressure, as long as you're under max. The Handi probably won't stand up to the 300 Win Mag or they would have released it (ok, if there had been enough interest).
Go to even lighter bullet weights & I'm sure you can go even faster, if that's what you're all about.
Sorry, I'm not Tim, but it just seemed like an obvious answer to me.