Those weeding tools (something which many people buy) always seem to break off some of the dandelion's root and regenerate. I would either buy some weedkiller as a gel and brush or mix weedkiller with some wallpaper paste and use that to paint the individual plants with. Might take a couple of treatments though.

I'd use glyphosphate [spelling? Roundup] with spray set to "jet" and squirt them

If in the middle of precious plants then a gel form maybe?

I would also use a systemic herbicide like roundup. if in the grass paint it on so you only get it on the leaves. though I noticed an ad on tv that suggested there is one that only kills the weeds and not the grass around them.

You used to be able to get a glyphosate stick that you could wipe on the leaves -don't know if its still available.

Don’t worry this is by far the best remedie which I have used for years, those awkward dandelions in between paving etc including thistles will be no more by using this method, all you need is cotton wool buds and a little bottle of diesel, then cut the dandelion to expose the cut stem then dab a little diesel on to stem, don’t drench it just dab it, it works really well on all perennial weeds.

Given that there's growing evidence that glyphosate is carcinogenic even though I've thought it was a good solution in the past, it may be safer to steer clear?
Applying diesel oil, salt, vinegar, etc. just kills the surface plant & leaves the root to come back.
Physically chopping away at them like you have been doing will eventually kill them but then there will be a new one nearby?
Could you not learn to like them?
I tried & failed to keep my garden clear of them but then I realised it was me not them☺ & en masse they're pretty & valuable to wildlife? Only thing I'm doing these days is going out with a plastic bag & collecting up the flower heads before they go to seed, which is a relaxing activity rather than letting them wind me up

Darren, now is the correct time to make dandelion wine, ideally pick them on St George's day [just a week late], make & enjoy it on Christmas Day

They do make a nice wine

Just to add, dab the the cut stem with diesel and the root dies back, tried and tested works every time, in my farming days when I was starting out the old farmer got me doing a field of thistles, useing a bilhook it was slice the base and dab with diesel.

GG, the French make a preserve from dandelions called cramailotte I think. I tried to make it once but as it only uses fresh petals it takes blooming ages (geddit?😄) & you'd need an acre & some nimble-fingered helpers