Rotten floorboard underneath block wall

Hi,
I have just gutted my bathroom after what looks like woodworm on one of the joists but also discovered the floorboard underneath the block wall between the bathroom and bedroom is rotten (about the first half length of it).
The wall is 2.44 wide and 2.5 high. The joists are 200mm (steel with timber top and bottom) and the floorboard is 18mm. Would it be OK to take bits of the rotten board away bit by bit and then place some joist in-line with it and make up the 18mm in slate like this:

http://www.selcobw.com/cembrit-jutland-single-slate-600mm-x-600mm/

My line of thinking is this could double up as support for the wall and noggins for the joists.
Another problem i have discovered is they butchered the joists in place to allow for the soil branch so i wouldn't be able to swop out without moving them. I am unsure if its OK to alter the block-work one-by-one as there would be no room for a strong boy to go in its place.
Thanks as always
Fats