Hi,
I don't know how much experience you have in this field, so please forgive any presumptions on my part.
As a rough guide, line-up levels for audio post are -20dBFS = 0VU (often -18dBFS = 0VU in Europe with dialogue peaking at -9dBFS).
You haven't made any mention of the clients delivery requirements / QC broadcast standards that you need to meet.
Also, have they given you any indication of where abouts in the signal chain the distortion is occuring (is it in the audio files themselves, or a product of overloading their system as a result of you mixing with too high a reference level - which could also make it dangerously loud).
If possible, listen to the mix in their theatre. It maybe that the artifacts from limiting are not as evident in your monitoring environment as they are in the destination environment.
Unless your documentary is about that new Russian Vacuum "father of all bombs" Bomb, featuring a ground zero POV of the detonation, I can't imagine what would require you to have audio anywhere near 0dBFS for any sustained period of time.
First of all visit
this page , then look at getting accurate
hardware meters.
You might also want to post this on the
Audio Post board .
Hope that helps.