"....I know how to create a melody in Vocaloid Editor 4, but after I have the melody, how can I integrate with BIAB so that I have a suitable backing track?.."

You can just save to wave and import to Biab ? or:

Vocaloid 4 should have a VST you load into the Host DAW, it also has rewire so you could try the ReWire plugin in RealBand http://www.energy-xt.com/index.php?id=0115
http://www.pgmusic.com/forums/ubbthreads.php?ubb=showflat&Number=371691#Post371691

https://www.kvraudio.com/product/vocaloid-by-yamaha

There was a ReWire mod for Vocaloid 3 http://blogs.yahoo.co.jp/alipapa_p/63025279.html use google translate.