My 1000A exhibits the same thing when I connect any of my AKAI's or the TEAC's thru the Tape deck preamps.
If your R2R is an Early TEAC 4010,and ONLY on the EARLY 4010's that were put together from a A4000S tape deck and a RA40S amplifier, the wiring is such that there will be 2 RCA cables on the back going to the pre-amp underneath. (The later models changed and these output's are now part of the umbilical).. 2 of these are marked Playback output, . You can disconnect the PLAYBACK OUT(L&R) from the tape deck preamp and run the Playback OUTPUT's on the TAPE DECK (not the preamp) directly to the TAPE HEAD jacks on the 1000A. Then on the Tapedeck preamp are Line IN . Connect these to the RCDR OUT on the receiver/amp. The umbilicals are used as normal. You'll be able to record but lose monitor ability from the tape deck (it works like a 2 head unit now.. I don't use the 1000A for recording so my early 4010 gets the nod here and I can use the TAPE HEAD connection as it was designed to be used. See below for difference.
Otherwise, with the Deck and the preamp connected Normally, connect it to the Tape Monitor from the Line out, and connect line in on tape preamp to amp RCDR OUT. But keep the levels on the R2R VERY VERY LOW, almost to ZERO!!!
The other alternative is to get an L-pad (1 per channel) and adjust so you can use the preamp normally or almost so adn the receiver/amp normally.
Scenario 1 (ONLY IF your Tape Deck is separate from it's PREAMP. EXAMPLE USED is TEAC A4000S with a RA-40S Amplifier combined to become a A4010.) Output is to AUX in the pic but use TAPE HEAD as there is no amplification and no EQ, which Tape Head postion provides.
SCENARIO 2; Note that the RA-40S Amplifier is included in the setup now. And the playback out is NOW RUN in to the AUX as the EQ is handled by the RA40S amplifier. You must keep RA-40 LEVELS down to almost ZERO to compensate for imbalance. This hook up is indicative of most tape decks/recorders out there.
If you get L-PADS they go in between the OUTPUT's from the RA-40S to the Tape Monitor on the Stereo Receiver/Stereo Amp .