That's unusual for a remington to shoot group that large. That notwithstanding, if it's accuracy that you want to improve, then I would first have the barrel re-crowned and do a trigger job, as this usually noticeably improves accuracy.
As for free floating the barrel, I have been told that the remington plastic stocks are such junk, that it is actually better to get a GOOD after market stock, like McMillan, HS Precision, or the medalist, and THEN do a free floating job. Again, most M7s, even with their synthetic stocks, are shooters, but I have been told that glassing the action, and thus free floating the barrel, on the cheap plastic stocks is kinda not worth it.
If you do the above, then I see no reason why your gun shouldn't shoot MOA or better with at least one factory load.
Zachary