My dad used to have an old (don't remember the manufacturer) small SIB with a rigid keel.
This boat had a 2-piece full length keel section made out of lumber (not plywood.) You attached the front 2 floor sections, and the rear floor section, and stuffed them into their respective seating positions, lined up the ends of the keel, and forced them down into a single plane. The joint was then fastened with a couple of U-channels surrounding the keel, with four through bolts running side to side. The remaining 2 floor sections were then installed.
As I recall, (and I certainly wouldn't work on this alone), the keel section was about and inch and a half to two inces wide, tapered from a near point in front to about 3 or 4 inches at the brow, then tapered back down to about an inch in the back.