Can I make one audio clip follow the peak levels of another clip across time

I am working on a classical music video that uses two audio sources. One was recorded using the venue's sound system using mics at the stage, uncompressed for peaks. The audio waveform therefore shows a beautiful sinuous pattern of softs, louds, and slopes between, and the performance sounds realistic, albeit realistic from an on-the-stage perspective. The other was recorded as part of the camera footage, taken from the back of the hall, to capture the ambience of the performance from the back-of-the-hall audience perspective; however, the camera automatically normalized all peaks, so that soft passages are louder than they should be and loud passages are compressed, resulting in an audio waveform that runs close to 100% normalization across time and sounds unrealistic. (I normally take my second audio source from a portable wav recorder, which also records uncompressed peaks, and mixing the two produces beautiful results, but I was unable to do that this time.)

I have edited both clips to be exactly the same length and have aligned them so that they start and stop at precisely the same points. The only difference therefore in the clips is that one has realistic peaks and valleys while the other has compressed and normalized these away.

So, I need a way to capture the peak PATTERN (over time) of the first recording and apply it to the second recording so that its waveform changes to LOOK LIKE the waveform of the first recording in its general sinuous shape. (The matching would be the general shape over time; one would not want to match frequency volumes millisecond by millisecond, because that would be unrealistic, since for example a timpani hit will sound louder and sharper on stage than at the back of the hall.)

Using Match Volume in Audition doesn't cut it, because I only get an across-the-board matching that applies to the whole clip. I cannot find any other sources discussing this, but it seems that with today's computing power and innovations there should be a way to do this. ???