No. Specific rings are specifically made for these inserts. However, I would caution against them. For one, the inserts are typically polymer, and polymer is quite soft & flexes more than most think. Also, I encourage you to go back a read again. It was mentioned that outside, mechanical scope adjustments USED to be the norm. Until a better way way was discovered. (Internal adjustment)
Here is a picture of a Vintage Unertl rifle scope. See how it’s adjusted? By separate mechanical Windage & Elevation adjusters. This is the same concept the Burris rings (and others like them), are offering. Seems like a novel concept, until one comes to terms it simply being a re-hashed idea from the 1800’s.
https://i.ibb.co/dr9mHkq/F61-CBABA-F...F9-E653329.jpg
Lets also not forget, the OP was convinced he had a major problem…that is, until he started shooting his rifle. He was able to sight it with his scopes adjustment range & it’s his top performing hunting rifle. All with some super-dee-duper Burris redu.