I'd still like to hear the results of the MP3 test...
If you want definitive proof one way or another whether the input pre's are where the issue lies, that test will nail it down... If the machine can't play an MP3 input into the line ins as cleanly as it can from the built in MP3 player (set up to the same volume) then there's the problem in a nutshell.
If so, pre-amping the mike won't make a lick of difference, it will be the entire input circuitry. But if it's clean and the same as the built-in player, then all your issue is is to get the mike level up to line level, unbalanced.
From hearing the distortion on some of your examples, perhaps the issue is that the arranger's Parts are too hot to allow for the extra headroom adding a beefy voice in as well produces..? Perhaps the solution is to turn down the Parts (or move the balance slider more to the keyboard Parts, then turn those down) so you don't have to jack up the mike so much?
I hope the solution is another unit, but I think there are things you haven't tried to troubleshoot the issue, yet...
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An arranger is just a tool. What matters is what you build with it..!