Tried the cabbage recipe again, wanted to see what different mordants would do. Shredded a full purple cabbage and boiled for about 20 min in 2l of water. I think it could take more cooking, there was still color left in the cabbage. Drained the liquid, divided into 4 jars, to try iron, vinegar, alum and baking soda. Final result:

Here are the eggs after about an hour in the dyes:These are iron, vinegar and alum. Soda didn’t really work much at all, so it’s not in this picture. Then I added alum into both vinegar and soda jars, to see whether that would improve how the color took. Left the one in just alum and vinegar+alum for another hour to achieve one more shade, left the rest for the night. Here is before taking the wax off, iron, vinegar, alum, soda (that one didn’t change at all after adding alum, and did not give a darker shade overnight, vinegar improved with alum, but the dye didn’t adhere so well to the egg):

So, I recommend alum. Vinegar and soda didn’t work very well for me, however, I used tap water, and it’s full of chlorine here, which might affect the dyes, can’t really be called a pure experiment. Use demineralized or distilled water if you want to make your experiment really “scientific”, and let me know how it goes.

The iron was OK, gave a decent gray after an hour and almost black after a night, but I wouldn’t use cabbage for that, unless you don’t have other options and don’t mind the cabbage smell.