My H&R Ultra Hunter/Varmint MC is fine with the scope height I have (old Weaver), the rear bell clears the hammer tip a comfortable tad. Higher ring/base combinations would likely not be right for my face. I dislike high rings; that tad above the hammer is always my key for fit as I dont want to 'chin' a stock, but 'cheek' it.
There are some 'stick on' cheekpads available that might work on your stock, too