Attaching a ledger board - only partial rim joist
The way I see it, you have two options to make things correct:


put blocking between them and a header joist over them to tie it together (It would be the equivalent of a 1-1/2 inch cantilever).  But you'd have to deal with siding over the little bump-out
cut back the joists 1.5 inches and put in a rim joist and splice it to the other joist with a tie plate.  Cutting back the joists will be a real pain.


I'd be tempted to just put in the blocking and sheet over it with something pretty good like half inch laminate, however I'm pretty sure that wouldn't pass an inspection.