Where to start? Where to start?
Okay, let’s start with the relationship between thickness and stiffness. It is not a linear relationship. Stiffness increases exponentially as thickness increases. I’ve attached a document that puts some numbers to it (courtesy of my friends at Saertex). Generally speaking, a panel that is built with a couple of layers of glass separated by a foam core will be stiffer than a couple of layers of carbon stuck together. Simply put, your laminate is going to be a whole lot stiffer by changing thickness rather than going for a higher modulus material.
On the subject of how to build and what to use, I’m not against experimenting with different materials but you should have a rudimentary understanding of the materials or you are going to waste money (but I guess education is never cheap :D). For instance, foam cores need to exhibit certain physical characteristics to fulfill the needs of the project. Is it cheap you are going for? Ultimate stiffness? Durability? There are many factors that go into the decision.
One of the myths of epoxy is that it will stick to everything. Are you sure your board is really PVC? Maybe it’s some other plastic. There are literally hundreds of formulations that can be made into board stock. There are also countless surface treatments that can be applied to that board that may promote adhesion or it could just as easily fight adhesion. There is no guaranty that epoxy will stick to something you picked up at the hardware store.
The bottom line is you can build stiffness in a variety of ways. You can increase modulus. You can increase thickness with a core. You can add geometry to the part. You can use a combination of all these things. Of course, the best way is often subjective so it’s not necessarily easy to say what is the “best” way. In order to figure out what works for you requires some education. The best and usually cheapest way to learn about materials is to lean on your suppliers. By suppliers I’m not referring to the lumber guy at the big orange box store. I’m talking about guys who actually know the materials and can offer cogent advice - composites salesmen at composite stores. One thing I’d suggest, figure out specific questions. Vague questions get vague answers.