The
jib trimmer should be able to handle both
winches if he's practiced. Tacking takes a couple of seconds. The lazy
winch should already have one wrap on it with plenty of slack in the standing end.
At "ready about", the
jib trimmer takes the sheet off the
cleat and gets ready to throw it off the winches (I'm only assuming this is possible on a self-tailing winch; no experience there).
In mid-tack when the jib luffs, the jib trimmer throws it off the winch and switches to the other side. He doesn't get in your way; you go
under the tiller when switching sides, not
over it. The main sheet trimmer stays forward of the traveler during the tack and preferably moves up to sit on the windward gunwale.
As the boat comes head to wind, the jib trimmer switches sides with everybody else and does the initial trim, then briefly goes up to put the first turn on the new weather winch (or asks the main guy to do this).
This is how we've done it on my boat, and how we did it on other boats I've crewed on when we only had one jib trimmer.