First, I can't get a grip on your concept without some kind of visual and a statement about what you are trying to accomplish would help, too.
I have read many discussions on building paddleboats with glass on plywood and glass on marine foam but never anything that combined the two. But there is nothing impossible about it.
In general, I would say you will play hell trying to make something even close to a top-drawer plastic fishing kayak. Fishing kayaks are the domain of rotomolded polyethylene. The shape of and the accoutrements of a fishing kayak, both on top and on bottom,are relatively simple to do in rotomolding. A mold is quite expensive but it's potential for complex shapes is unparalleled. They can make hull shapes that are near impossible in any technique based on plywood and/or foam.
Next, foam core may have a few design advantages but one of them isn't light weight. Glass on foam suffers from lack of resistance to penetration and the only way to get that is to use sufficient glass and a lot more epoxy which increases weight quickly. Epoxy is about 9¼ lb. per gallon. Thats more than the weight of water. Also, marine foam is very expensive and the rule of thumb is a foam cored hull will cost about twice as much as it's glass and plywood counterpart.
If you are thinking about using houshold insulation to cut cost be advised it has already been done but has never caught on. I think it's because the stuff crumbles if subjected to a lot of flexing.
If you want to build your design by all means go for it. But don't expect to build anything that competes head to head with what can be bought, currently. The pros have designers that are conversant with the mysteries of hydrodynamics. They have the know-how and the technology that can make a big stabile fishing kayak paddle fairly well for it's width so you can go way out there and tussle with very big fish and not end up in the water yourself.

: I just found this forum and have a question. I have owned several plastic sit
: on top kayaks and used them for fishing the Galveston bay system for
: years. I would like to make my own but am not sure the idea I have would
: work. Cut a piece of 1/4" plywood for the floor, use foam to build
: the sides up about 6" and put about a 4" piece of foam on the
: bottom. After shaping I would fiberglass it. About how much would one
: square foot of fiberglass weigh if applied heavy enough make the boat
: rigid?