What distance are you planning to shoot at?
If 200-300 yards don't worry about it and just try whatever projectiles you want. If over 200-300 yards you need to start considering twist rate and projectile weight.
I've found that it's not till you get out to where it is slowing down (velocity and RPM) that you need to start worrying about spin.
I know, that's not what the internet tells us but I've done testing of my own and done a lot of reading and have found that at short range your groups will change with different projectiles and powders but almost any projectile can print a decent group from a decent barrel at 100 yards if you find the velocity node that brings the barrel into the right harmonic to release the bullet in the same place in the barrel whip every time.
I have a 12 twist barrel in a 223 bolt action and it will print tight groups with almost any projectile out to around 300 yards but beyond that it falls apart completely with heavy projectiles because it doesn't have the bullet RPM at the muzzle to maintain enough spin to remain stable as the distance increases.
Regardless of twist the bullet is stable leaving the barrel and for up to 200-300 yards, after that is when you see the stability go away when the projectile and barrel twist are not suited to each other. In extreme cases like shooting an 80gr projectile from my 12 twist it just doesn't work well at any distance but a 9 twist should stabilize any projectile for a couple hundred yards, after that it might make it to 300 yards but only testing it will tell you for sure.
So, if you do try some 70+ grain bullets make sure you test them at 300-400 yards if you find something it seems to like at 100 yards.
Of course it's your rifle and money so feel free to do whatever load development you want with your rifle and I hope you find a load you're happy with but the reality is that (in my opinion and as you've mentioned) you bought a cheap bullet hose. I would enjoy it for what it is and if you want tight groups replace the barrel. A decent barrel will transform your rifle for very little money. Jerry from Mystic Precision has a Norinco AR with an aftermarket barrel in it and he has completed the black rifle accuracy challenge with it. The groups are very impressive and all he did was change the barrel as far as i know (he may have changed the trigger as well).
Not really sure why you want to shoot more expensive ammo from a Norc but there's nothing wrong with trying to find a better load for any rifle. I would be looking for a nice load with 55gr projectiles, maybe a 62gr if you can find a bulk bag for a good price.
Again, unless you plan to shoot at 500-800 yards you don't need to have a heavy bullet with a fast twist barrel. A 55 grain bullet can shoot nicely out to 400-500 yards.
Good luck.
