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Remember that transom height is just that, the height of the transom, not the length along it.

The old 13 footers have a transom that slopes backwards about 20 degrees. I've measured these old boats and the length along the transom from the keel to the notch is a little over 21 inches.

Going back to our highschool geometry we know that a right triangle with a hypotenuse of 21.25 inches and the top angle of 20 degrees, will have an altitude of 20 inches. This is the transom height.

If the Honda BF30 measures 17.5 inches from AV plate to mounting clamp (and this is the typical measurement of small 15" short shaft motors) then it leaves the AV plate about 2-1/2" above the keel.

I certainly would not rule out the possibility of the this motor working on a 20" transom Sport 13, especially if a good cupped propeller were used.

Its easy enough to try, mount the motor and see how it does. It will quickly become apparent if the motor ventilates or not. You don't have to worry about cooling water; the motor will loose grip l o n g before it looses cooling water.