The Problem With the Upstairs Floor

This crude diagram shows a cross-section of what the "joists" are for the second floor. For some reason, someone lapped 2x4s over the 2x6s to raise the floor for about 2/3 of the front end of the house. The first floor is solid and has a subfloor, but the second floor deflects and bounces because of the shoddy joists and having no subfloor.




So, what do we do? I'm working on that now with Pat.

Originally I thought of merely reinforcing the joists somehow. But when I discovered there was no subfloor, I decided that ripping up all the floor and replacing bad joists was the way to go. This would mean a lot more demolition, purchasing new joists, sub-floor, and finished floor.

Pat suggested that the existing floor could make a good subfloor; now we are back to the original idea of just shoring up joists. But how?
Replacing them by sliding new ones in from below - without cutting into anything like the floor or studs in the balloon (the house is balloon framed) is nearly impossible. If the joists are 16' (192") and they are spaced at 16", resting on 4" at either end, the diagonal of a bay is then 186.7" , which is 7/10 of an inch longer than the length of the bay.
Removing another joist to make the diagonal longer does not help, either, for the bay is also bounded by the studs in the balloon.
Anyone out there with good puzzle skills?