Your images help loads. As you have found out it is obviously one of the very uncommon inflatables with a wooden keel not just a DIY idea.
From your image of the keel remnants at least you have the greatest height of the wood in the central area and location of the join so you can copy that in a length of plywood. You can also see that the tapers (where the ends have been in the fire) are different with one being a slimmer profile. This will go towards the transom.
It will never be economic to have this made properly and finished but if it suited you could get the overall rectangle of wood cut at a timber place then refine the shape yourself.
If you base it on the height of the bit you have and make it overlong then you will have to trim down by trial and error.
You could of course make up a trial piece from a piece of cheap softwood or chipboard then once you know the fit is spot on copy it in a piece of decent plywood.
The way I would get an idea of the height/profile would be to inflate the boat to full pressure with the tubes supported so the floor could hang down then with one section of floor missing at a time measure the height of the keel needed at each side of the opening so you can transfer these measurements to the new (or trial) keel.
You should be able to work out how long the keel was from rub marks on the inside of the floor where the old one sat. I wonder if at the bow the keel engages with that notch in the front board. I assume that board is fixed into the boat?