There is a lot you can do with the MIDI melody track. Personally I would export all of the MIDI tracks into Logic but if you don't want to do that I would bring in the melody track as MIDI and rest of the tracks as wavs. Note I am suggesting you do all of your work in Logic however you could just modify the MIDI track in Logic and import it back into BiaB. Your choice.

As for your magic sauce there are a number of ingredients you can use. Humanizing would help as well as adding vibrato and pitch bend. These I would start with and probably would do the trick for you. If you are still not satisfied you could add volume automation, various effects and effects' automation, effects like chorus, a touch of distortion, delay, etc.

Whenever I get something stuck in the back of my throat, I dislodge it by drinking a beer.
It's called the Heineken Maneuver.

64 bit Win 10 Pro, the latest BiaB/RB, Roland Octa-Capture audio interface, a ton of software/hardware