[Revision of earlier post. Added info regarding "pan law" bug* in FCP.]
I have seen this article before, but I need to create a multitrack QT not an MXF. Also the change in audio level we're seeing is 6dB.
Since you didn't go into detail about your FCP configuration, I thought that article might be helpful. The process should be the same, except for the output preset/settings. You might try outputting an MXF with your project and check the levels in the result. It's been a couple years, but when I followed the article's workflow things turned out fine.
The idea is to use that article as a guide. I can't recall why 3 dB is mentioned in the article. There may be something different about an MXF file compared with a multi-channel QT file. You could do a test with 3 dB and one with 6 dB.
However, I do know that there is a "pan law" bug in FCP (if things haven't changed since version 10.4). It causes levels to drop by 6 dB on imported clips, which is what you're seeing.
"typayton" discusses this in this article:
After doing a small test, our audio house said that simply raising the level within FCP by 6dB before rendering the master file is not a good idea, as this is altering the specs of their original audio tracks.
Changing the overall levels to compensate for the flawed pan law implementation in FCP *isn't* changing the balance of the mix. The audio guys need to get a life (they are being a bit precious). As long as they deliver the proper mix to you, that's the end of their responsibility. Enough said (maybe too much).
If I had had more details about your situation, or your level of knowledge about the issue, I may have suggested doing a "global" 6 dB increase on the audio and see how that works. That would be if the directions in that MXF used as a guide for your case didn't work out (you may be doing a similar workflow otherwise).
Of course, this situation underscores the need to test all parts of the post workflow prior to the start of post/editing. Running into this kind of issue near the end of a project can be very costly and stressful to everyone involved (it sucks).
Another option would be to export a finished, "pre-mix" version of the project as ProRes 4444 (XQ), or whatever, perhaps video only, and bring that and the mix from the audio guys into DaVinci Resolve (Studio) and marry them there for final output.
* I refer to the current "pan law" implementation in FCP as a bug because it's rather non-standard (and since I referred to TPayton's article).
Here's a good article that talks about how audio gets processed in FCP:
Is Your Audio Mix Too Loud?