Derivation of Maid, Maidli, Meydli
Unless I'm really missing something, German Mädchen is not a descendant of Proto-West Germanic *magadīn. Rather, German Mädchen is from German Magd + diminutive suffix -chen. German Magd is descended from Proto-West Germanic *magaþ.
Also, English maid is not derived from maiden, but is instead descended from *magaþ, same as German Magd. Meanwhile, English maiden is descended from *magadīn. The etymology currently given in the maid entry appears to be incorrect.
Well, it seems that this overall topic is somewhat more complex than I thought. So according to the answer from Eiríkr Útlendi, the following Mädchen entry in magaþ is also incorrect.
It would be really great if someone with a linguistic background can check & correct the whole matter.
However, at least the following derivation should be correct:
Alemannic Maydli is from (old?) German Mayd + diminutive suffix -li. So, the Alemannic term Maydli is effectively descended from Proto-West Germanic *magaþ.