Hello!
So most morphs for axolotls are recessive. The only non recessive are basically what you have listed as dom… I’m assuming “dark” means wild. It’s generally just called wild type. That’s the basic default color of an Axolotl, but it has a huge variety. GFP and RFP and genes introduced by people that make the animal glow under a black or blue light. From what I’ve discovered following the geneticist Strohl, at least with GFP there is a super version. I guess you’d call it a dominant gene, since I believe the super and non super look about the same (though there can be variation in the amount of glow in any of them). The difference is of course that the super should produce all GFP offspring, and you get them from pairing GFP x GFP. I have not been able to test this but I’m working on it myself, I’ve got a GFP x GFP pair and waiting on eggs. I would think RFP is the same, but that’s much less common and I don’t know for sure that it follows the same pattern.
The basic recessive morphs are this: melanoid, axanthic, golden albino, white albino, copper, and leusistic.
White albino and axanthic are definitely separate genes. Albino and golden albino are linked and I personally just for hets say “het albino”, because depending on the pairing and their genetics you can get whites, goldens, or a mix. It’s very complicated and explaining how that works is difficult. They’re connected, but two different morphs.
Each morph has variations. For instance, you list dirty leusistic as a separate category. A dirty leusistic is just a variety of leusistic, like a bluegill leusistic is. You can breed them to have higher pigment in their face or gills, various different genes work together to make these differences, but they’re still leusistic.
Lavender in my experience is usually use for a light melanoid or axanthic, and I’ve noticed in both cases they’re usually het leusistic which I believe helps with the lighter color. Though I’m not sure that’s a defining trait explicitly.
Piebald is a variety of leusistic. It’s basically an extremely dirty leusistic. I would keep all leusistics in the same category. If you can give them sub categories that is okay. But you could breed a high dirty leucistic and still produce babies that aren’t very dirty or dirty at all. So making them separate might be confusing. I already get people thinking dirty and regular leusistic are two different genes 
I’m not familiar with enigma.
Silver dalmatian is I believe a very light silver colored wild with spots. They’re selectively bred to be that way. As I said originally, wilds have a lot of variety. I’ve got one that belongs to someone else in my house right now and we’re going to breed it to a het axanthic because we’re not sure if r dal is actually axanthic or truly a wild like I was told. You will also see things advertised as green wilds, which are particularly green animals… Light wilds… Dark wilds… Starburst (high iridiphore wilds). At the end of the day, they’re all wilds, just like all those leusistic types are all leusistic even if they’re bluegill or dirty.
Copper albino is a combination of copper and albino. Not one morph. Both are recessive. A lot of gene combos in Axolotls are actually kinda hard to tell apart. A copper albino for instance would be kinda hard to tell apart from a regular copper. Though you could tell a copper melanoid apart, or copper axanthic. But copper leusistic? Not really. People call red eyed leusistics “copper leusistics”, but from my research, they’re often just leusistics with red eyes. Usually their eyes are blue, but they can be red. A copper leusistic looks almost identical to a regular leusistic so many of the combos you will only know by knowing the genes of your animals or breeding them.
You have other variations in some colors such as HW (high white) and HI (high iridiphore). Iridiphores are the shiny spots on some axies. They are not on every morph. I believe mostly just wilds, coppers, and goldens, though I could be missing one. If a large part of the body is covered in these shiny bits, they’re considered high iridiphore. With goldens that’s called sunburst, with wilds it’s starburst… I think coppers is moonburst but I’m not positive. Some morphs also have high white variations, especially goldens. That’s where a large portion of their body is very light or white. You can also have pink goldens (I called them rose golds). They’re fairly uncommon, but very pretty. They are goldens with a pinkish look. I’m sure that’s not all the variety for the different morphs but it is a good bit! These variations are not recessive, but are based on various genetics at play other than the basic morph. From my discussions with Strohl, my understanding is that it’s not often just one gene that creates bluegill or many other varieties. It takes several genes working in the right way to get certain things. That’s why I identify them as the base morph, and consider the extra genes just variations in the basic morph. I feel to classify every single gene and variation would get highly confusing and complicated. So you have several varieties within most of the actual morphs.
There’s also something called mosaic, which is basically the Axolotl version of a paradox. You have split mosaic, which is when they’re pretty evenly split down the middle two different genes. I don’t remember what they call the mosaic that’s not split but it’s where the two genes are scattered all over the body rather than split. Mosaics are usually very expensive and highly sought after in the Axolotl community.
My suggestion would be to add a category for each basic gene and then subcategories for the different varieties if that’s possible (leusistic > dirty leusistic), but I’m not really sure if that’s what you are going for or not. Very awesome to see y’all working on so much. I’ll see if I can get anyone else to comment, and if I think of more I’ll add it or edit.
I was certain you had bred them in the past, so it was worth a shot asking.