Remington Model 34

I just purchased an old model 34. They were made from 1932 to 1936. It's pretty banged up and the the bluing is near non-existant, but it shoots tight groups.

The problem is, that it shoots consistently five inches high. The elevator on the rear site has been removed, for the obvious reason, that shots are way too high.

Does anyone have any suggestions as to how I can fix this problem, short of filing down the front site?

Please comment!