So with the Lux stock and those high rings you would need a Giraffe's neck to make it work, and you don't have one of those. You are a no neck guy like me.
Even with the stilts, you still can't get your thumb in there without risking pinching it. In fact from the picture, lower rings would actually give you better thumb clearance. Rings are cheap, mount as low as you can for the scope you choose, lows or mediums. Even with 6x24 Scopes on my Rimfires, most of them mount up fine with low rings.