I've been thinking about this all morning and finally I noticed something. I've the TRBX604 and a BB424. They are very different, in plugged in sound, in unplugged sound, in weight, in neck. I love the sound of the BB, but am appreciative of the very easy neck of the TRBX.
So much for the 4 strings. You've pointed out that the TRBX605 has the same neck specs as your BB735, so you would get no additional benefit there. So you would get a lighter body and 3 extra frets, but against that would be: no through body bridge, no 6 bolt join, and two very dull pickups. Does that sound tempting?