All you need is overhead projector sheets of clear plastic and sikaflex.

Wrap the film around the leading edge of the new board (about where it penetrates the bottom of the hull) so that the film matches the surface nicely, put board with film into existing case, fill the gap at the bottom with sika maybe 1" up into the case, wait for sika to cure and remove board, clean up bottom of the new case flush with bottom of hull...

Make sure the new board is pushing against the back of the case, the sika won't take the loads from the trailing edge as well as the back of the case will.

I've seen it done on a competitive 12' skiff. Looked very neat and tidy. It was only about 1cm thick of sika though...