My Folks, or more appropriately "Santa Claus", gave me a Belgian Browning BLR for Christmas of 1970. That .308, with it's light, 18" barrel, would put five rounds into little teeny tiny groups that a lot of heavy barrel rifles would envy. Most enjoyable was 130 gr. Speer HP's over 45 gr. of 4895 when it sold from Skagg's for .49 cents a pound in a paper bag that they measured out of a Hodgdon keg. Using that load, I'd keep shooting prairie dogs way out there when the .22 centerfire guys were having fits trying to get hits beyond 150 yards. I later "stepped up" to a 700 Remington with a 22" barrel, and it would not give the same accuracy, nor for that matter, match the velocity I got from that 18" barreled Browning! To paraphrase from a loading manual "that's the reason ballisticians go prematurely gray"....
I wouldn't touch a rifle that was giving the kind of performance you're getting from that long, heavy beast, but instead, would go down and take a look at one of the Marlin short action .308 bolt guns. Around these parts, they go for $339 or so, sometimes with a scope, and the two that I've had would shoot every bit as well as my old Browning, and with a helluva lot better trigger. Their light barrel just won't do it all day long after the barrel heats up like a heavy barrel will.