I believe you have 3 options. The cheapest option is to use the scope you have. I shot good scores out to 1000+ yards with a .30/06 sporter loaded with match bullets with a 3-9X40 Bushnell in Weaver mounts. Yes it lacked target turrets. Yes it lacked sufficient elevation adjustment, so I used an aiming target above my impact target. Yes the cross hairs were too thick, so I needed a 4 MOA aiming point. All of these things made me want a good long range scope, so . . .
Option 2 was to purchase a high quality scope in used condition. The good scope brands stand behind their product regardless of how many owners they've had. Leupold has the edge here with a Canadian warranty center.
The third option is to wait until you can afford an appropriate new scope.
Don't waste your money putting a good scope on a good rifle with poor mounts. A cheap scope mounted on a good rifle with good good hardware can shoot, but an expensive scope on a good rifle will only shoot sometimes if the mounts are flimsy.