Honestly, if it's only for 100 yards, what you have should be fine. Most stock guns that aren't "match rifles" shoot 1.5-2.75 MOA. That means 1.5-2.75 inch groups at 100 yards.
The .223 is very capable of hitting targets out to 1000 yards, it will have about the same amount of energy as a .22lr, but it can be done. It all depends on the nut behind the gun.
Now, there are 2 words in the AR-15 world that don't go together, those words are long range, and low cost.
If you are thinking that you would like a more accurate gun on a budget, have you considered just replacing the barrel. It's pretty easy. On a budget I'd recommend putting a good barrel
on it, and installing free floated handguards to meet your budget, and you will need a rifle length gas tube. You can use the same gas block. You can get a pretty accurate setup with $400 by doing this. You don't have to buy a separate bcg, charging handle, upper receiver, etc.
If you really want a separate upper, look at a PSA Upper minus BCG and charging handle
And just use the bcg and charging handle from your other upper with it. And you have some money left to save for a free float handguard.