In 4th gear (1.00:1) at any given engine RPM, changing the rear axle gear from 4.22:1 to 3.89:1 will cause the actual vehicle speed to increase by
8.4% without affecting the speedometer reading. If "a 14 tooth speedometer drive gear on the tail shaft" refers to the gear on the transmission end of the speedometer cable, then changing from a 14 tooth gear to a 13 tooth gear should increase the speedometer reading by about
7.7%. The number of teeth on the speedometer cable must be a whole number, so 13 teeth is as good as it gets.
I have no idea where you could source a suitable 13 tooth gear or if the S-V speedometer cable-end gear can be readily changed. In the 1960's, it was common for U.S. car makers to use easily interchangeable speedometer cable-end gears, but I have never heard of Rootes doing that.
As Mike noted in post #2, there is a gizmo called a speedometer calibration gear box that can be custom made to correct just about any error.
https://speedometercablesusa.com/gear_box_adapters.html
https://www.ihpartsamerica.com/store/SPEEDO-GEARBOX.html
In theory, you could re-calibrate your current "built ... out of three spares" speedometer by reducing the spring tension on the dial side of the "speed cup". No idea how practical that might be.