Well, I'm not much into created names... my opinion is that if you really like
Ava, popularity shoudn't affect you. Avah is just like
Ava, the -h at the end doesn't change anything at all.
Aveline, or Avalyn is nice, but Ariava, Avanna etc. are just too much for my taste.
Another suggestion is
Ada - it sounds almost like
Ava, but not that popular.
Avalon might work as well.
"After all who of us in our lives hasn't set fire to some great public building or other..."
Graham Chapman