Well actually I'm sitting in front of the computer writing this.

The most unique I've seen is Mal Falconers, he sewed the bottom back on (with I think aramid thread). I guess he injected some resin first, and soaked the thread in resin as he sowed. He drilled holes all the way through the board along the centre line and ground out a bit of a groove for the thread. I saw this when I was at Sandy point in 2010, as far as I know he's still using it.
I've done the resin, vac bag job, but there was so much damage to the internal foam, the bottom ended up with a lot of hollows, I had a fair bit of bogging to do to get it reasonable. But the board's still going after approx 5 years.
The best results I've had is what Mike's proposing now, replace the damaged foam and create a brand new bottom. The hard thing here is getting a dead flat surface on the old foam, so you get a good bond with the new foam, with no voids or a thick layer of resin. I'd left the bottom intact around the fin box where it seemed the box had held the board together, and forward of the start of the nose rocker, where that had also held the bottom down. As I wanted to recreate the original bottom as close as possible I also left the rails intact, so I was working in a well.
If you're making a completely different bottom, probably easier to cut the whole bottom of level.