1. Retile starting from bath up (use wood shims or match sticks to space
tiles off bath) like most people do.

Too late for that. I would have to take down and redo nearly three
walls.
When I was laying the tiles, I initially tried using tile spacers to
space the tiles off the bath. But they couldn't support the weight of
the tiles. So I ended up shoving part tiles underneath to give a solid
flat base. Unfortunately, when I removed the part tiles, the gap was
bigger than I anticipated.

2. Put shims under bath legs to raise a bit so reduce gap.

The bath is screwed to the wall, using 2 brackets. And the brackets
have been tiled over. Shifting the bath up would probably cause this
to move. What do you think?

Any gap bigger than 1/4 will work its way open pretty quickly as well as
looking crap.
Looks like a sealing strip is needed. But try to fill the void first
with silicone, or tile adhesive, or something(!)

Thanks
Mike