MPI stocks in Oregon makes stocks for right handers with a major cast on for a left hander, light weight for hunting. That's the only way you can use your left eye in a right handed stock, definitely not what you want.
To shoot the groups you are looking for. You will have to shoot 100% in a supported position, prone or on a bench period. From those positions, you can shoot an appropriate rifle for the task right handed with no problems.
Close your left eye until the right is in full focus in the scope, as long as you can maintain focus, otherwise wear a patch on your left.
If you were hunting, that's a different scenario. The last thing you need is to close one eye, cut your field of view in half. Lose depth perception/depth of field. Time to find and engage.... will also be hindered.
If I understood your optic choice a fixed 10x44mm with a 34mm tube. You can hit targets at 1,000 yds. but not consistently to your desired specs. Granted you have more adjustments with the 34mm.
10x at a thousand yds. is 1x at 100yds. Meaning can you shoot at a 100yds with a one power scope and get 1.2MOA consistently. Personally I would look at a top end of 18x-25x. Granted weather permitting with mirage and air currents.
Find a 1,000 yard range and watch what the shooters are using in equipment and they usually are friendly with advise. Maybe you can shoot one of their rifles for feel.
I am right handed left eye dominant and only shoot left hand rifles period. no matter the discipline. You will quickly adjust and thrive.
Best of luck to you.
