Repair cut in sidewall of tubeless tyre
The solution to fix this was in the Pinkbike article suggested by @Batman in the comments to the question.

If you buy a radial tyre patch designed for a car then chances are it'll be plenty big enough to patch a hole in a bike tyre. I just went for some cheap ones on eBay. Add the vulcanising glue (plenty of it) to the inside of the tyre and stick the patch on. To be extra safe I added some glue around the edges of the patch after it was in place too.

As you can see in the photos below, there is almost no noticeable bulge on the tyre.

I've ridden the bike a couple of times since reinstalling the tyre and it has been flawless, no problems with the tyre and you certainly can't feel the patch when you're riding.




I realise there is no single solution that will work for everyone who finds themselves with a cut on the sidewall of their tubeless tyre but this solution worked very well for me.