I think it is best to set the levels correctly during the recording/digitizing stage.
I did some tests amplifying files in WavePad with good results, but there may be other factors with your situation that I cannot really duplicate.
Have you actually tried to amplify a file with WavePad? The software can be downloaded for free, and then you can do some experimenting yourself.
I use the program to clean up and edit all my digitized recordings of lps before burning to cd. Works great!
Best of luck.