Anwyn is definitely not a Welsh girls name. Names ending in 'wen' are female, names ending in 'wyn' are male.
I know an Alwen (female) and an Alwyn (male). Anwen is female. As are Olwen and Bronwen. Bronwyn is often suggested on here but it is a misspelling and mispronunciation of Bronwen. Olwyn is the Welsh word for wheel and very much not a name. The 'wen' and 'wyn' in Welsh names have real meaning and are not interchangeable. Unfortunately people do get them wrong sometimes when naming their children.
OP - I have one of the names on your list. Born and raised in England (Welsh mother). I love my name and don't regret it, but most people say it wrong initially and need correcting. Most of those people still say it wrong after being corrected. It doesn't bother me much, but it bothers my mother. Feel free to PM me and I'll say which it is privately.
I hope to use Welsh names for my children, subject to DH's agreement!
I like:
Eira - (EY-ra, ra as in rabbit. I can live with EY-ruh, my own English accent defaults to ruh for ra in names like Lyra and Lyla, but it may bother you)
Tesni - (TESS-nee) means warmth from the sun. I love this, thought of it as soon as I saw Glesni on your list
Morwenna - a Welsh-born saint who did her saintly stuff in Cornwall.
Alys (Alice) - I love this spelling, doesn't have the 'lice' element of Alice
Nia - I worked with one and most people managed to say it correctly
Ffion - I love this but my aunt used it for my cousin - the Ff may cause issues though
Seren - (SERR-en) my husband really likes this. I know my mother doesn't as it's quite a 'modern' Welsh name. Pronounced correctly it's gorgeous, but it may become Sair-un.
I think the most beautiful welsh girls name is Esyllt, but it won't work in England due to the Ll. It's the Welsh form of Iseult.