I've never kept axolotls and honestly don't know a lot about their habits, but I would think that a plant carpet and axolotls don't go together. It seems to me the axolotls would constantly uproot the plants. However, many of the plants you listed can be grown attached to rocks, wood, etc., rather than buried in a substrate so I would suggest that you use pool filter and as a substrate. If you really want to try rooting plants in the substrate then you could try soil capped with sand. Again, I don't know if axolotls tend to dig in the substrate, which could be a problem if they're kicking up dirt all the time.
Have you succumbed to the pleasure of Multiple Tank Syndrome? I feel your pain!