I bought an HW100s that came with a Hawke 4-12 x 50 scope on Sportsmatch medium mounts. It only had a 25mm tube and did not have AO which kept the objective bell smaller in diameter.
I still found the comb too low to provide a decent cheek weld and correct eye alignment with the scope.
I eventually found that a Hawke Vantage 3-12 x 44sf mounted on Sportsmatch low mounts just cleared the barrel and sat low enough for my alignment.
The objective bell on the 4-12 x 50 was 57mm or 63mm with the bikini covers in place.
The new 3-12 x 44sf is 51mm or 55mm with the covers. I did have to grind a groove in the cover to clear the barrel.
Both scopes have 25mm tubes.
Hopefully some of those measurements may help with your calculations.
I suspect that you are correct and will need high mounts but you may need to address the comb height too.
Best of luck!