It's hard to tell from that photo, but the transom looks like mahogany. White oak would be likely (and good) for the keel/keelson. Be careful now that you've taken out a lot of components - if the boat relaxes and changes shape on you, it could be very difficult to get it back into its original shape. But push on. The boat looks in good condition overall, and anything can be replaced or repaired with forethought and care. Your original transom can be re-built, it seems, by splicing in a bit and re-glueing the original components. Hang in there. This is a great place to ask questions, to get feedback from those who have been there before, and to receive emotional support when needed in your restoration journey. Particularly with your grandfather's memory as a driving force, the journey can be fun and the rewards great.
Good luck and enjoy,