Patching subfloor with pre-existing furring strips?

I’m trying to see if I could try and do this repair on my own. I know what caused the damage, as it was a refrigerator with a leak that lead to one of the corners sinking into the floor. I watched a few videos on how to take out a bad area of subfloor, how to increase stability of the surrounding joists, and to install new plywood and I felt really confident. When I did a quick look at the damage at first, I felt better doing it as the damage was in between the floor joists. Then I tore the tile away, I noticed there is either furring strips under the plywood.

Now I’m not so confident. The 2.5 in wide and 1 in thick boards go throughout the house looking at it from the basement. They are not interlocking, as I could jiggle a putty knife between healthier boards. I don’t plan on tearing up the entire first floor to eliminate the wood strips from this 1900 home, and was hoping to do a patch job only instead of doing the whole kitchen. I was still trying to determine the thickness of the plywood over top. Is it possible to replace the furring strips between the two joists and it still provide strength to the floor? Distance joist to joist is 24 inches. I’d hate to put in the effort of the planks and the plywood for it to be too weak for the weight that will be there.

I wish I could provide better pictures underneath from the basement. There isn‘t a light source there and I’m still not very bright with the flashlight.