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Paducah said.. >>>this would have been a good time not to use a plywood as half the plys aren't helping you: the grain is not aligned with the stress. Plywood's virtue (other than being less expensive) as a building material is that it is relatively uniform in strength in different directions so useful as a "skin" - floors, roofs, etc (yes, it still has a "grain" in many sizes as the number of plys are odd). A laminate where all the plys run in the same direction would be a different animal. But, this is the fun part of the process: learning how and why things are the way they are. Good luck!
What you say is true, but I don't think that's relevant. If you're relying on the timber's tensile strength, it's going to snap!!!!!!!!!!!
It needs either glass or carbon fibres to take the tensile loads, the timber should only be there for compression.
My recent fins have been end grain palm, before that end grain balsa. This is where timber has it's best compressive strength, but end grain balsa is hard to shape, it's density varies too much. The end grain palm works a treat though, only problem is thin sections are very fragile, (the advantage of ply). I shape one side, then glass over it, before shaping the other side. This holds it together.
Not sure you could get a single piece of end grain palm big enough for a foil though, it would probably need to be joined.
Here's some picks.

so fin marked out and a layer of 4oz cloth over the top.

Using a tiler's profile gauge to check the foil.
And here's the carbon cut out ready for laminating on