If the recording is important enough to you to put the post-production work into it, and if the noise isn't audible during most of the musical sections that are more energetic..
1) Duplicate the recording to additional channels in the DAW. Keep the two copies identical for the time being and automate a cross fade between them just prior to each time the noise becomes objectionable, and back again to the original just after it becomes unnoticeable. If you were to listen to the output at this point it would sound identical to the raw recording (the cross fades are being made back and forth between identical copies).
^You are now setup to try a few different things to fix the noise problem by applying whatever you do to only the copy that is cross-faded to during the noisy sections. Whatever treatment you apply will only affect the noisy parts of the recording, the parts where the noise is not perceptible will not be effected at all.
2) Try applying noise reduction in Rx. Tweaking settings for minimal artifacts. lf it works decently enough you are done.
If not, try instead..
3) Whatever other noise mitigation technique you want (such as coping over only effected frequency region from the good channel). If it works you are done.
(with either of the options above, if you can reduce the noise somewhat yet not sufficiently to keep it from being objectionable mostly because it is only on one side, you can try adding a little bit of noise to the clean side. The noise will then at least sound balanced rather than lopsided. Like a cassette. Retro analog. If acceptable, you are done.)
If not try instead..
4) Monoize to the quieter channel during the noisy sections. The recording will cross-fade from noise-free mono during the quiet parts to stereo during the louder parts. If acceptable you are done.
4a) Try applying pseudo-stereo techniques if you like. The recording will cross-fade from pseudo-stereo during the quiet parts to stereo during the louder parts. Tweak the pseudo-stereo with an ear toward minimizing the difference in spatial feel during the transition to and from real stereo, rather than seeking the most attractive pseudo-stereo effect on its own.