what to expect in my situation

i'm the owner of a model 16flhss in 7wsm.
being left handed i cannot find an aftermarket stock for it, so i reinforced the original
tupperware with an aluminum plate and devcon and bedded the action.
since it's my primary hunting rifle i want to keep the hinged floor plate and the sporter style stock.
now i've been reading a lot about prefit barrels and was wondering if i can expect good accuracy out of them even if i keep the original stock?
some say they only clean better but don't offer much of an improvement accuracy wise.
some other say it's a night and day improvement.
i'm only a hunter, not a pro shooter. but i like to shoot and i practice out to 600 yards.
with the factory barrel and reloads (150 g scirocco, 67 gr imr 7828) the typical 10 shot groups are
7 shots in .7-.8" and 2-3 fliers that enlarge that to 1-1/4".
being somewhat a novice to reloading (4 years) amd learning to shoot without a mentor. i have a hard time figuring if the fliers are due to the shooter ( most probably), the load,the barrel,or the stock/bedding?
since i like to thinker with the thing, i'm planning to order a prefit barrel to try and improve my setup

what do you pros think?

sort the flyers when you get one. then scale the brass to see if it is different.

your groups are how far. guessing not 1.25 at 600

Sorry if it was not clear, they wwre at 100 y.
Thanks for the tip

Nothing wrong with those groups, especially for a sporter-weight barrel and 10-shot groups. As for fliers, as Blue mentioned it can often be a variance in case weight/capacity. It can also be a number of other things such as bullet runout, weak primer, inconsistent powder charge, variance in neck tension, etc. In other words, they can drive you nuts if you let them. Rule out the easy variables and if that doesn't eliminate them just chalk them up to something beyond your control - life's too short to get stressed over the occasional flier.

You could get a laminate stock, and do your own relieving for the bolt, etc.
I found that the aftermaket barrel could take shots a little closer together than the sporter barrel mine came with. Also the extra weight made it so it didn't smack me around so much making me relax for better groups.

Kevin Rahill at Stockade's Gun Stocks will make you a nice lh stock. You might give him a call 308 432 5114.

You might also talk with Jim at Northand Shooter's Supply, he is very, very well versed in aftermarket barrels and sells the best ones out there. He also sells stocks, may be able to point you in the right direction 763 682 4296.

For what its worth I have bought a number of barrels and stocks from Jim, and one from Kevin. I've also owned a number of factory Savage barrels. All of the factory barrels I've owned shot well. All of the barrels I got from Jim shot really, really, really well.