Another way to do it is to infuse one side using a sheet of glass or mirror or something like that. Just a flat sheet of carbon. Then bond on your core using a strong epoxy adhesive. Then infuse the second side over the top of the core so that it covers your edges as well. One thing I would recommend with that method is to use some 2" wide carbon tape or 2" strips of carbon and cover the edges, then lay over the full thing. Also when you lay the full sheet, cut snips in the carbon at each corner so that you avoid pinching the fabric when you bag it.
I have done this successfully, albeit on a smaller scale building 1sqm sheets with a 10mm divinycell core. I don't see why it can't work for you.