I love my handi rifle in .223. It shoots all day long inside an inch. Great little shooter as I'm sure your 7-08 is. 48 gr of H4350 does sound a bit hot and is evident in the description of your brass. If I were you, I'd back it down a notch. My browning Micro hunter 7-08 loves 150 gr spcl bullets from Cabelas pushed by 46 gr of IMR4350 which is also a max load. Both IMR4350 and H4350 although not interchangeable have very similar burn rates.
Drop down a grain or two. A critter will never know the difference. And to extend your brass life, if this is your only 7-08, just back your sizing die out a bit and neck size your brass. This should improve your groups too.