Type 9 speedo failure? Mine caused by worm gear drive ( friction fit only ) sliding along the tailshaft. Various advice sought which included chemical grabber eg Loctite or a spot weld on the tailshaft. Neither perfect, grabber has minimal surface area to adhere and a spot weld has issues in future dismantling. Opting for a drilled and tapped M 4 grub screw hole started diagonally from the worm gear edge thus avoiding the plastic toothed speedo drive. The grub screw registers in a 4 mm dia indent drilled into the tailshaft. The grub screw secured with grabber and a centre punched indent on the worm gear edge. I suspect my Quaiff Pro tailshaft might be dimensionally out causing the friction fit problem.

Isn't the worm gear for driving the speedo?

Oh! - should have read the question more carefully!
So yes - I'd change to a digital speedo, driven off a wheel.
Been on my 'to-do' list for years...

Then just glue the old worm gear in place to stop it moving, and causing any other issues, after removing the rest of the old speedo drive gubbins.
Gain more BHP too!

https://www.merlinmotorsport.co.uk/p/racetech-80mm-electronic-speedometer-rtsc130

And for once the L7 forums is actually of use:
https://www.lotus7.club/forum/techtalk/5-speed-gearbox-speedo-drive-gear-what-holds-w orm-output-shaft