It is possible to remove the core, and then reglass leaving a small sump area. However this will not be any deeper than 3/4" or maybe even half an inch after properly re-glassing. If you went this way--you would cut a circle, then bevel the edge at about 45 degrees, relaminate about 1/4" of biaxial cloth around the edge of the core which was exposed and the bottom, spreading this out a bit into the inner layer of the hull (in prep for this I would grind out a gradual slope of 1/8", so there is not a build up around the cut out.
HOWEVER--I would put a false floor in--using foam. I would use a fairly low density foam, maybe 3 to 4" deep, then put your "sump" where ever you want--I would probably make radial grooves to that sump--and then put your dri deck on top of that. Even 2" would work if you don't have the room for 4" foam. With this I would use 3 layers of 6 oz cloth--the reason is that you want to work the cloth smooth into these grooves, and the sump. You may have to do a little cut and patch, as well as some fairing with medium density filler, and cabosil mixed in the epoxy as a finish before painting or putting truck bedliner as a coat. (the latter preferable). You can use a small router and carbide bit, with circle cutter for cutting inner layer--that way there is no chance to cut thru the hull. Works better than Dremel tool. I would not "finish" with 5200-there are much better products for that, unless you need a sealant or adhesive.