Hope the eSHa 2000 treatment (suggested by Fishlady) is helpful.

[You don't mention filtration (which processes the fishes' waste), but presumably you have that too?]

Absolutely delighted to read this - thanks so much for the update.

Apologies for being unable to reply before now, and for my brief reply.

How is the situation now?

When unsure whether to medicate (especially with other tank inhabitants) or for what condition, I sometimes dose a small amount of API Melafix which can "tide things over" for a bit and sometimes even resolves them.

Fingers crossed for your black moor. Keep us posted.

Apologies for only seeing this message now, and many thanks for helpfully providing a comprehensive background.

I would treat for velvet/slime disease such as eSHa Exit or Waterlife Protozin.

Keep us posted.

PS. I tried to edit my post above but the edits vanished.

Treatments such as eSHa's gdex or alx, Waterlife's Sterazin or Parazin, or Interpet's Anti-Crustacean Parasite are likely to be best. Check their descriptions and internet images of what they describe and see what seems to be the best fit.

Looks like some sort of external parasitic infection which will need treated ASAP (along with ensuring that water quality is at optimum levels at all times which is crucial to reduce the risk of any medical problems). Check weblink here: [to follow]

For water quality, use a liquid-based test kit such as API Masterkit (not strip-based tests) and ensure that ammonia and nitrite are consistently at 0 ppm and nitrates no higher than 20 ppm above your tapwater nitrates level.

Glad to have been of help, and thanks for the update.

Your theory sounds 'spot on' - and your treatment for it too. Well done!

Keeping everything crossed that this fully resolves and that your weather loach returns to her usual self.

[If of any consolation, I've also "been there" with a decor problem that only revealed itself after the event - it hadn't occurred to me beforehand; fishkeeping does seem to be very much a "live and learn" hobby.]

Sorry for the late reply.
It does look to me like it might be an ulcer (although I'm not familiar with that species of fish), and you've been undertaking the correct treatment that I would have done (although I rarely find an improvement after 3 days and often have to extend the treatment by a couple of days and then wait for a few days to see if there's a latent effect/improvement).
As the water quality is fine after the move (presumably you moved across the filter media so there oughtn't to be too much of a swing in water chemistry), what may have happened is that she's struggling to adjust after the sudden change of environment incl less biofilm in a comparatively immature tank and consequently may have injured herself in the process such as darting around to try to get her bearings or hiding herself in strange locations (such a you've already described).
Personally, I've had some very good outcomes and complete turnarounds with Melafix in recent years on other fish (much more than I've ever had with actual medications), to my surprise and delight. I would have a search to check that it's compatible with your tankmates (eg I think surface breathers may struggle with it or require extra water-surface agitation).

Sorry for the late reply.
I completely agree with Fishlady. However, if you preferred not to have neons again, similar fish such as cardinal tetras or green neon tetras would probably be fine alongside your lone neon.
[A personal anecdote: Currently, I have a lone cardinal tetra, having decided not to re-stock as they have never done well in my tank and assuming he would die soon after the others. To my surprise, he has been thriving, pottering around either on his own or with some of the ember tetras (but not with the rasboras). It might be that yours will be ok alongside other tetras.]