You did not state which bases and rings you went with.
I have the Warne two piece bases on my Savage 12FVSS in .223. Chose those because it was a .223 (not going to go very long range) and it makes loading from the top easier than a one piece. I used Leupold Mark 4 steel rings.
The critical element is to make sure all the screws are torqued down properly, and to lap the rings. I've used several lapping bars, but the only ones I own and use now are the Kokopelli Products accurizing kits.
The rings must be perfectly aligned to your particular setup, and no two are the same. Lapping them is the only way to ensure you don't have any torque being applied to your scope tube. Precision optics don't have an acceptable amount of allowable "give".
But no matter how you slice it, it sounds like your current setup was done in a shoddy manner.