I had the same issue doing bodywork on mine last summer. I bought it with a bed full of wet leaves and unfortunately that was a more solid floor than what was underneath. My sides were fine though like yours.
Some info that might be helpful from my experience: If some parts of the floor are OK, I'd reccomend cutting out the bad sections and doing patches, and by patches I mean you can have one 4 feet long, I did, and you can get 4 by like 2 foot I think patches with the ribbed Ford bedfloor pattern from either Summit or JCwhitney for like 25$ a piece. I thought about doing the whole floor, but some problems I ran into were, the floor is alot of the structure of the bed, and if you take the whole thing out, the rest may just fall apart. Also, the floor is welded to all the crossbars underneath, and tearing up the whole thing, from rusty weakened crossbars will be horrible and can also do damage.
I'd say as long as you can weld, put some patches in, even if it needs to be half the floor. Mine came out really nice.
AleX