I had something like this in my mind, but I've never tried it. In a DAW,
duplicate the transferred audio on two parallel tracks. Flip one out of
phase and mute it during the desired audio. During moments of print-through,
fade up the other track. It hopefully will cancel the echo, but only
minimally effect the uncorrelated tape hiss. You might filter the second
track to concentrate its effect on the particular band(s) causing trouble,
in order to minimize weird coloration of the hiss or ambience spectrum.

Would that actually work in practice? Labor intensive, but there might be a
way to semi-automate those crossfades. Otherwise, maybe Malcolm's idea of
working from full-volume signals is more effective. If somebody will upload
some test audio, I'll give it a try. None of my tape machines work right

If science doesn't work, offsetting the second track enough to overlap
background during the moments of echo would make for an easy way to
crossfade to non-echo moments, yet have consistent background noise spectrum
at those moments. Much easier than editing-in clips of noise/ambience, while
the shape of the crossfades can be used to smooth the transitions.
Multitrack is very useful in ways beyond just mixing tracks in the
conventional sense.

-----Original Message-----
From: Association for Recorded Sound Discussion List
[mailto:[log in to unmask]] On Behalf Of Malcolm Rockwell
Sent: Thursday, October 24, 2013 10:51 PM
To: [log in to unmask]
Subject: Re: [ARSCLIST] Advice needed on removing / minimizing tape

There may not be a major problem here. What has printed through is the audio
from the next layer of tape, correct? With digital manipulation being what
it is today it should be simple enough to grab the full volume layer of
audio, attenuate it, flip the waveform and apply it "over" the printed
through signal. There will probably be artifacts but if you fiddle with
various parameters for a while, such as EQ, you will probably be able to
find an acceptable solution to your problem. I'd apply this to softer
passages and leave louder material well enough alone, though.
It's worth a try.