Can't comment on Amiga programs but CoolEdit2000 on windowse has automatic function for bacground noise elimination... It requires user to give part of recording that has nothing important and then automatically eliminates (some... confiurable) of that noise of full sample.
Anyhow.. I have not been reserching it any more detail so
I've no idea how it'll exactly does the trick but it'll seem to work quite good.. Most likely it analyses known noise and creates filter (fir?) for eliminatig it.
So.. yuor method could indeed work.. at least with some cases..