Is it safe for the ChaCha8 nonce to be deterministic?
Yes, it is safe. The only requirement for the nonce in Salsa/Chacha is to be unique; being predictable is not an issue, so a counter is fine.

Like CodesInChaos indicated, I believe extending XSalsa20 to XChaCha20 would also work if you want to a larger nonce, but have nothing concrete so will leave the details to him/her.