The KayakPro Namu I would think would be a contender for fastest recreational kayak, the small version 13'6", the medium 14'9". Take a look at the hull and you'll find clues to what might make a 14 footer faster or slower. The fast boats seem to tend to avoid any concave surfaces in contact with the water, including along the sides leading to the bow and stern ends. They typically will have the plumb bow and stern as you see on the KayakPro Namu to maximize waterline. You might see the bottom of the hull rounded clear to the ends, instead of tapering off into a sharp v, or even more resembling a fin for some distance near the ends. I think these might be some things you could look for in evaluating recreational kayaks for potential speed to thin the herd before deciding which ones to test. But there's a lot to how you want the kayak to track, and the stability you require, and endless other considerations, and that's why you find so many different approaches.
Unfortunately, you may not find KayakPros around, and they may be pricey compared to what you're thinking of spending. But I thought I would offer it up as something to look at as an example of a fast 14 footer.
Recreational Kayak Paddle
Touring Kayak Paddles
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