My scopes tend to be mounted a bit further back than what you have there.
The distance from butt to trigger is about 350mm (10mm shorter than you) but the scope is 250mm from the butt, so about 2" closer.
Unfortunately you are going to need to compromise somewhere as the current scope/ring setup gives you almost no room for adjsutment, a common issue with long action rifles without rails.
Basically you will need a rail or a different scope with more mounting space but I'd say that Leupold is probably better than most.
I'd get a picatinny rail and some low rings, it shouldn't end up much higher or heavier than your current setup, but it looks as though taller rings may be required anyway if you end up pulling your scope back, as the objective bell will be getting close to the barrel.
I find I always need a cheek riser, even with a small objective scope mounted as low as possible. All my Tikkas with factory stocks I've ended up installing a cheek riser.
Whether you need a cheek riser depends a lot on your face structure, I've used some peoples rifles and can't even look through the scope because the cheek piece is so high.
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