Solid Hardwood, Engineered and Laminate Flooring - (Help!) Repair 80 year old hardwood floor

Ok, I just bought this house that was built in 1922. It has oak hardwood floors that have been nailed down with pairs of nails every 5" or so.

The dining room has a lot of squeek, and some areas have "bouncy" areas. In addition, some of the screws have started to pop up.

I had planed to either renail the bad areas, or possibly insert screws from below (have access via an unfinished basement).

I just inspected the floor from the bottom. There are 9" tongue in grove boards running at 45 deg to the joists. The wood floor is nailed directly to this. The subfloor boards are really old. There are 1/8" to 1/4" gaps between some of them, and a few of them are cracked.

Pulling up the floor and putting down new wood is *not* possible w/in the near future (cleaned the bank out to buy the house). What options are there for adding support from below? Can I run sheets of wood underneath, screw them up into the wood floor, then maybe secure them to the joists? Should I just put some 2x4 or 4x8 between two joists?

Thanks!

Correction:
I just found a spot where there had been a laundry chute cut. It appears there is a layer of 3" or 3.5" tongue in groove boards under the oak. These run parallel to the oak boards.