The cleats definitely look like a copy of Mariner-style rigging. In your situation, I would skip all the extra hardware, and run a painter from one cleat up through the toggle loop and back to the other cleat. I did something similar on the front deck of a skin boat a while back.
Here's the Mariner inspiration, from their website under 'Model History':
And my version:
The length is adjustable using a sliding knot, and it passes through a loop of bungee at the bow to tension it:
If you think about it, a double line up the middle of the deck is only a few inches from where a perimeter line would be. The cleats will tend to elevate the line a bit, making it easier to grab.
A painter turned out to be more useful than I would have guessed. I've used it to tie multiple boats to a dock as mine was the only boat that had one.
Also, the two carabiners unhook and drop straight down to the tow hook on my car - magic tie-downs that are always in the right place.
The Mariner system is actually a continuous loop of line that passes through the centers of the cleats. I prefer to have the ends detachable to allow the tie-off options.
The Kayak Wing
Kayak Motor Kit
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