your carpenter should be able to cut out the rotten area back from the wall enough to slip a new piece in there. He'll probably want to cut it back enough to be able to nail a couple of blocks between the joists to give him places to glue and nail to on all edges.
It shouldn't be either difficult or costly to fix this. If the rot extends too far underneath the bottom plate of that wall it will be slightly more complicated, but still quite reasonable to repair, imho.
Good Luck! 
EDIT: Looking at those photos again...you'll probably want to get that old floor mastic off of the subfloor before you re-tile. Not sure how easy that will be on particle board. You might want to check one of the floor store in your area to see if they can tell you whether it's ok to skim new mastic over the old stuff (but that will raise the level of the new floor).
Like Warpy said, doing it the right way now is a pain (given your circumstance) but it will be more of a pain if the job either fails, or the results are unsatisfactory.
Again, Good Luck!
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