Have you looked at a Sig 716. I am thinking of selling my M1a socom to buy a 716 or an LWRC Repr.
Bought an M1A several years ago, found out the accuracy was not up to par so had a Master Armorer from the Small Arms shop at Crane do a make over from one end to the other. Now with the old M1 bullet [all separated by ogive into lots] it's a MOA shooter.
I have an AR10 Armalite, Lots of AR15s, M1A1, and bolt guns in the .308.
Seeing what you already own I might suggest the bolt gun.
I carried the M14 for over a year and a half and I loved it. The M1A1 is a good pretender but falls well short of the original. I like mine but other than the "nostalgic-cool" factor it's just another semi-auto.
It's not made to "tacticool customize" with over the counter goodies but you can play a bit with them. Decent shooting rifles, heavy, ammo isn't cheap unless you roll your own, and just in case of the SHTF-EOTWAWKI evolution, it's going to be a beast to hump along with your other necessities.
Bolt gun for good accuracy, cost effective, and honing your shooting skills. Master the longer bolt shots and the rest are easier.
I will say that if you ever get around to shooting the M14 style rifle, you will fall in love with it, especially open sights. And weight is not really as much an issue with it as many say, in standard form it's just over 9 lbs.