I faced the same dilemma a couple of years ago. My 1903 had an old German scope on it which, although usable, was not ideal for my aging eyes. I decided if I was going to change to a modern scope it had to be done "right".

Here is the result -

I'm very happy with this set up. It did mount the scope a bit higher than the original but I just use a strap-on comb raiser and it's fine.

Cheers.

GG