The gun shoots well but I think it's capable of better and I'd like to enhance the set up with better optics. I'll likely use it only for punching holes in paper at between 100 - 300 yards.
You think the rifle should do better and it's right off the scope .................Hmmmm have even considered that it might just be the rifle?
So to my mind the first thing to do is beg, borrow or steal a proven scope of known performance and put in on top of your rifle and try it again. If the rifle does better in grouping then yep you need a better scope.
If on the other hand there is no improvement your just going to have to face it that you either:-
1) need another rifle that does group well
2) your going to have to stump up money to fix the rifle you have.
So then you have to decide how much your will to sink into this.
Of course one did not mention nor ask are
YOU the shooter actually capable of shooting small groups?
It's amazing how everyone thinks they can and are the best there is yet when it comes down to it most of us are just plain ordinary.
How many of us can truely learn to use high magnifications properly?
I also find it strange the modern shooters need scopes the size of Hubble to shoot 100-300 yards. Our eyes must be much poorer than out fore bears.