Free: Contests & Raffles.
If you were really wanting to keep it a cheap budget rifle, I'd use the cheap existing scope base and rings, but JB-weld them together. I'd JB weld the base to the action (careful to keep JB weld out of the screw holes). And then Possibly JB weld the scope rings to the base too. If you careful wipe away the excess it'll hardly be noticeable unless you look carefully, or try to take it apart, and it will give you confidence that it isn't moving.There's nothing wrong with what you are doing though, and by most people's opinions, what you are doing is the right way to do it. It just costs a little more money.
4 of my kids have Savage Axis rifles.They all shoot somewhere between good enough and really good.The only mod I've made was the M CARBO trigger kit.It's only like $20, and it reduces the trigger pull about 40-50% which really helps.Did you shoot it first just to see?They're not works of art, but sometimes they drill holes in the right spot pretty good.
Sorry that happened to you...my son's Axis .270 drives tacks once we sighted it in. Maybe we lucked out
I'll be curious to see how it shoots.