Repair large-ish area with core

I've got a couple cats with damage, one of which has two areas ~1' sq that I had to cut completely out (1 sq ft after grinding, cleaning up, tapering, etc).

I'm curious what my options are if I want to try to include some core material in the repairs. I feel like I'm going to add a non-insignificant amount of weight if I make every repair solid, so on these large two I'd like to save weight if possible. However, I don't have any rigid foam, and these areas are fairly curved, so it seems like a rigid foam core would be somewhat labor intensive.

Are there liquid alternatives? I'm thinking a glass bead fairing filler in epoxy would have all the properties I need, aside from being expensive, but I have tons of it. I also have expanding urethane foam, but I haven't seen any info about using it as a core material.

It also looks to me like some balsa core sheets are flexible (like 1"x1" tiles)...if that's the best way to go I can do it, I'm just trying to avoid ordering stuff.

I know these are likely fairly basic composite questions, but I've never done any layups with cores, (just simple repairs and cradles) so I don't know what's possible and what isn't..and I don't have any core material on hand.

Thanks for any advice!

In the past, I've used the damaged sections to piece together and shape a repair patch.

http://www.teamseacats.com/2008/02/19/a-crushing-defeat/
http://www.teamseacats.com/2008/03/03/fiberglass-repair-by-airmail/

It sounds like it may be a bit late for this method. I would probably find a similar section of hull to build a quick and dirty mold from. I would layup the outer skin and then build it inward. I'm not sure what I would use for the foam core, but I would probably try to source some real foam core used in boat building and of the same thickness as in your hull (someone has to have a scrap piece). It can be heated and bent to shape probably with a heat gun over the back of the skin piece in the mold. Once shaped, glue that to the skin with epoxy/microballoons. then build an interior skin to that pices. With that done, cut the patch piece to fit your hole and use the wood stick method (in those links above) to get the patch to fit. Then taper the seam back so you can build glass from the inside out in a thin area around the seam. Fair, and finish.