Repair Top of Rotted Floor Joist
nightsurfer: cool handle BTW.
If I understand you correctly, 50% of your 11' long joists cantilever outside the house.
It appears that you have a slightly different code requirement for cantilevers than we do here.
We are permitted 1/3 of the joist length to cantilever, so in the case of a 12' joist for example, only 4' could be outside.
Are the existing joists pressure treated or not? Doesn't sound like it.
I must wonder if two are gone, how far behind can the others be?
One other point, do you have an exit of some kind going from inside the house directly to the deck? I would guess you likely do.
We have a requirement here that the surface of any adjoining deck must be a nominal 2" below the inside floor. That means that when we cantilever a small deck, we must use a 2 x 10 joist. The top of the outside portion has 2" cut off the top. Thus leaving you a 2 x 8 outside.
I think if I were you to avoid any future problems, and I think I can see them arising, that I would remove the existing deck and use the proper footings and posts with appropriate beam to carry your new p.t. joists.
A deck up in the air is no place to mess with. You will be much happier when it is done right.