Thoroughly clean the barrels bore and chamber.....Then,
I would free float the barrel first. Your barrel might be a better shooter, might not... you won't know until it is free floated.
Personally I don't like the Quad Rail Cheese grater hand guards... (no offense, and to each his own )
But make sure whatever your hand guard choice has a decent amount of ID room for an Adj. GB.... any contact between the gas block and handguard negates consistent accuracy. So allow for barrel whip room as well.
Then Try a box or 2 of 168gr FGMM out of it... IMHO, that ammo is pretty much a standard for .308 ammo.
Do not assume your first 5rd groups to be indicative of the accuracy potential of your barrel... I believe ammo needs to "season the bore" ( 5-10rds ) prior to shooting for groups.
I have slowly seen groups tighten up when changing one brand/type ammo to the next.
Not every time, but enough to believe in seasoning a bore to the next test ammo.
Then a better trigger... you can shoot good groups with a USGI spec type trigger, it just requires typically much more concentration.
Then if you want a better barrel, consider spending 350+ ish on a well respected barrel manufacturer's product.
And by this I mean, Ballistic Advantage and Faxon make good barrels... but a additional 100bucks will go a LONG way towards "increasing your odds" that your barrel shots well.... I have great respect for Criterion barrels.
IMHO , that extra spent now money is a bargain in the real world... you might spend that much just trying to make a lesser barrel shoot to your expectations.
If it is "over-gassed" , an Adj. GB will help quite a bit in taming the perceived recoil impulse.
Buy a quality click adjustable GB. ...those set screw ones, will work.. but ( IMHO ) are fussy to tune/ set.
If your barrel has a .750 gas journal size... make sure the replacement barrels gas journal is the same size to save a few bucks down the road if you decide to upgrade your barrel.
308's in this price range typical benefit from a Adj. GB, especially in the perceived recoil, and feeding wise.... easier on you , easier on the fired brass, easier on the parts, easier follow up shots.
If you decide to change the stock to a different carbine one... Limbsaver makes a couple of excellent recoil pads for various Magpul carbine stocks.... FAR, FAR softer then the OEM Magpul ones.
Bottom of the link... 3 different ones. And have proven to be plenty durable.
https://www.nokick.com/AR_15_Stocks_s/127.htm
Please keep us updated as to your progress !