The tetras see the betta fin as a chinese buffet, they will nip no matter how many are in.
I've had some luck with simple colored female guppies and pristella tetra. Stellas have very tiny mouths and they loathe tipping over to take bites, you can get them in regular and gold. They get to be about 2 inch max and easily live 2 years under betta conditions.
What I've done since Goat got half-eaten (all but a bit of his fins) by the neons is simply put a tank beside the tank for Fluffy so he can watch the pretties. It wouldn't be a stretch to give the betta four gallons of the ten with a clear divider and put a mix of neon, cardinal, glow light and black neons in the 6 section. Remember to keep six caracidae (neon like) minimum, they will shoal and be happy.