No, you're right, interface mixer settings shouldn't matter to levels inside the project.
But we still don't know what your Source selection is for bouncing/exporting, which is a major factor in the result you get. If you bounce a single track to another with Source = Tracks, I wager it will bounce at the expected level. If not, somethings's going on with gains, offset mode, mono/stereo interleave, mono/stereo track format, pan law or... something.
Assuming a single track bounces at the correct level with Source = Tracks, then you need to look at the bus I/O levels (both software and hardware) that get involved when you use Buses, Main Outs or Entire Mix as the source.
Another possibility if it's only synth tracks that are changing level is that the rendering process is producing a different level than the live output. Try freezing synth tracks first, and make sure the levels are not changing at that point.