I built many kayaks and canoes back in the '80's. Waaay too many really.

The most common method for stiffening the bottom of a fiberglass canoe was to use something cylindrical, or better, half cylindrical, down the centre line inside, and glass over it with a couple of layers of fibreglass, usually CSM. The core is incidental and just there to form the shape. It could be a bit of rope, or better still a shaped piece of PVC foam, but usually I used thin plastic conduit tube about 3/4" to 1" diameter and sliced it in half to make a upside down half cylinder shape. Don't forget to thoroughly sand the bottom of the boat to help the resin adhere to it.
On lightweight competition Kayaks, I often used a stip of 4mm Corematt with a layer of glass or carbon cloth over it to make a sandwich, but I think a PVC foam stip, a feww mm thick would probably be stiffer and absorb less resin, and be even stiffer again if it was shaped in a half cylinder. This was often done in conjuction with transverse ribs of the same construction in the widest part of the hull. One consideration is how stiff you actually want it. On whitewater kayaks we didn't want to make it too stiff as the hull needed to flex a bit over rocks etc. That is why we used a flatter rib profile and Corematt. If you make a rib too stiff it may delaminate from the hull if it gets loaded too heavily.

Glass fiber is very good in compression so don't get too carried away with other exotic materials. Just make sure it is thick enough to give the shape the required stiffness.
Edit: I just had another thought. It might be lighter to use a slice out of a sheet of corrugated fibreglass roof panel to form the shape. Sand it well on the side you are glassing over though!!