even with a sling, heavy is heavy. you dont need a heavy barrel to be accurate. i have an m700 mountain rifle, and its 3/4 moa for 2 shots in a row. then the barrel is too hot. i could quickly and easily put shots on target with it out to 300. beyond that, youre pushing the 7-08's capabilities, imho. for live targets you dont want suffering anyway. i can put a scope on an m16a4 and hit with confidense out to 500 yards, and thatll still be lighter than your sendero. 500 yards isnt too far out there. a sendero in '06 should take you to 1000 if you can handle it.
never carried an m1. done my time with a m249 (15#) an m240g (24#) m2hb (84# receiver and barrel) and a mk19 mod3 (72#). can you top 72 pounds unloaded (not including the tripod and cradle) with an m1? no such thing as a sling for the m2 or mk19.
just checked remington, you cant get a sendero in '06 anyway. i dont think you ever could get it in 308 either. its their long action magnum reciever. does come in 300 win mag though. besides, its a totally different class than the 710 and they shouldnt be mentioned in the same sentence.