I suspect what you are trying to accomplish can be found under Fitz's post in this link.
viewtopic.php?f=4&t=37627Also, if your just prototyping, I am in favor of making things from scraps. This way, if it does not turn out like planned, it wasn't any loss to you.
My personal perspective, I've been trying to make a successful axe since I started Foam Smithing, The leather core makes it quite heavy, and since its an axe it will already be by nature top heavy. The design you have I tested and determined it just did not work. On paper, it seems solid, but in practice the foam does not have enough torsional rigidity when laminated like that. I do strongly suggest you pursue Fitz's design, it seems solid and he has reported great success with it.
On note of the top heavy aspect, fighting Florentine with them is going to be different than using regular swords, and a vast difference from speed bats. To get an idea of it, it will be like swinging a sword whose balance point is 12" from the tip, rather than the hilt. I would attach some weights to the tip of one of your spare bats and swing it around at home to get a feel of what its like.
All that being said, have some fun with it if you decide to proceed, and cut out a cardboard blank in the shape of the design you want to see how it will look once finished, a lot of proportions look good on paper but end up needing adjustment once you choose to build.