Off the cuff, I'd say go with a heavy-barreled version of the AR-10. There's no new design work needed and there are several manufacturers, so Uncle (i.e. all of us taxpayers) will have the advantage of competition to lower the price. However, sometimes it pays to think about solutions to a problem with a clean (or cleaner) piece of paper. Toward that end...
Does anyone know how accurate the XM8 system is? If it is accurate enough in 5.56 mm out to 600 yards or so with the longer barrels, then adapting it to shoot 7.62x51 shouldn't be too difficult - it is supposed to be a modular system. The rifle uses an op rod instead of a gas tube, so there will be no fouling problems (I think that I saw somewhere that it has run for 15,000 rounds without cleaning and without any jams).
Further "clean sheet of paper" thinking leads one to a round firing a 6.5mm bullet. These have about the highest BC's out there, and I know that ballistics data for the 6.5 Grendel round show that it retains more energy to dump into a target than a 147 grain .308 out past about 500 yards (and about 95% of the M118's energy at that range). Take a look at the article at
http://www.65grendel.com/ dealing with using the 6.5 Grendel in the M249 as a LMG cartridge. Also, with the high sectional density of the 6.5mm bullets vs. just about anything else, it makes a good round for penetrating cover (which is certainly needed on the battlefield, as opposed to punching holes in paper targets at the range).
Here are a couple more interesting articles discussing the 6.5 Grendel:
http://www.65grendel.com/faq.htm Check out the ballistics chart there (it is a downloadable .pdf), which shows that the 6.5 Grendel stays supersonic out to at least 1,000 meters in all of the 108, 123 or 147 grain loadings tested, while the M118 is only supersonic to 950 meters. You want your bullets to stay supersonic up to the target, as coming back below the barrier disturbs the flight path (i.e. it degrades accuracy, not a good thing when shooting at someone who can shoot back).
http://www.65grendel.com/art005newdevs.htm
http://www.defensereview.com/modules.php?name=News&file=article&sid=600
By the way, I'm not associated with any company or individual that makes the 6.5 Grendel rifle or ammunition. I just think it is a better round than anything out there for nearly every purpose imaginable, and if adopted for both the everyday infantryman, the designated marksmen and the sniper crowd, logistics would be enormously simplified. Further, I'd love to see the round adopted, so as to make it and the associated rifles/uppers cheaper for us in the general public to obtain.
