Final update on this.
Shortly after the last post, he said he was currently on a big job and couldn't attend for 3 to 4 weeks to do the repairs. I begrudgingly accepted. 4 weeks came and went without contact, so I complained to Checkatrade. They sent over a surveyor who agreed it was substandard and needed ripping out and starting again. Checkatrade suspended his account which finally forced him to give a full refund. From what I have heard, he apparently tried to get the negative review removed too, but they refused, which has put my mind at ease that other customers will get some warning of his workmanship.
I ended up redoing the job myself just focussing on 1 valley per day and it's looking pretty good - admittedly not perfect artwork, but pretty smooth and relatively straight with no bottlenecks like there were before. I used a decent mortar mix with SBR and plenty of it under the tiles to get a good bed, so I know it's at least sound and will get us through a few winters. Probably want to look at dry valley in the long run.
Redoing it myself really showed how much of a cowboy job it was. He hadn't removed any of the loose old mortar at all - just pointed over the top to make it look done. He hadn't even cleaned or brushed out the valleys beforehand - piles of dirt behind the pointing. Some of his pointing was bonded to moss! In some sense, this was a blessing as it meant his stuff came off with very little effort! He's also pointed up to the top faces of the tiles and over the drain channels, so any run off was being directed behind his pointing anyway. It was just so much worse than I thought originally, and I knew it was bad!