I go the other way around from the OP, but I don't have my band any more, just 2 hands. Since the "song" is the thing that flows with ups and downs and pauses and such, I do my guitar + vocal at the same time first because this is the part I play live, and I can feel my own song flow better doing them at the same time. The bass gets added as an overdub and fills it out. Finally the drums are the last bit. Once the guitar and bass and voice are in place I find it's an easier bed I can follow on a drumset and put accents where they belong and follow the tempo feel changes of the origional guitar/vocal part.
If I don't like how it blends together, I just redo the first guitar/vocal part along to the overdubbed bass/drum parts that played along to the origional; Redo the parts from the origional guide track rhythmically to the tracks it guided. eh. works for me well enough and there's nobody else to argue with me about it (which is why I have to do it this way anyway).