The rifle looks good.
Keep an eye open for a Griffin and Howe detachable side mount for a 7/8" scope. It is similar to the mount used with the 32TP scopes. Base might have to be made or remachined. Would require drilling and tapping, of course, wouldn't do this to a good rifle.
I have a good shooting bitser LB, and have thought about doing the same thing that you did.
There is nothing wrong with a Lyman Alaskan scope.
For my simulated 03A4, I used a Weaver 330. Badly bubba'd 03A3 was the candidate. Its a much better sight than I would have thought, for scope with a 3/4" tube made in the '30s.