But What About The Joists?

Problem solved, at least in theory. The joists are 16' long, and they rest on either end on platforms (I lied in previous posts; part of the house is balloon framed, the front end is more like platform). These platforms are 4" wide at each end. The new joists only have to overlap 2", so the piece I need to stick in can be less than 16' by 2" on either end. This gives some wiggle room to stick the new joist in at a diagonal.

Much thanks to Pat and Dave (I think he helped on this) for the advice.