Result! Roofer was back in and I am much happier with the results now, at least from the way it looks.
The second light point in my video took a bit more of convincing, but he did relent once I brought him up in the loft and showed exactly how it looked - that slate simply wasn't right! He had cut a completely random sized piece of slate and wedged it in there. All the slates appear to be correctly sized now, there is still some light gaps, but they are comparable to the rest of the roof - i.e., not actual spot lights, more faint lines.
The sealant on the last slates was a hill he was ready to die on, though. He was very confident in it's capabilities and longevity, even when I mentioned lead tags (I've been reading...)... He said the sealant was mostly being used to fix the tile in place, not stop water ingress. I thought I had pushed him enough at this point, either way, I can't see any more sealant bleeding through the loft, so happy with that.