From what Ive read below, I think I love the idea of Gray most, especially since it references your mum too!
Here's my other ideas:
For Anthony
Annie
Annette
Anne
For Gary
Ary/Arie (ah-ree)
Ree/Reah/Rea (pro. like the second half of Gary)
Corin-same meaning as gary: spear
https://www.behindthename.com/pnl/145466