Is reverse NTRU still secure? I'm currently prototyping something with the NTRU encryption scheme but I wish to use it in "reverse" -- distribute private keys so anyone can decrypt, but keep the public keys secret and thus only allow certain entities to create new messages. Is NTRU still secure under such a scheme? It seems from the literature that chosen-ciphertext attacks using decryption oracles (which essentially every entity would have) have had some success in breaking traditional NTRU. In general, does knowledge of the private key give us any information about the public key?
No, this system is not secure. Knowledge of the private key immediately gives enough of the public key that we can immediately encrypt an arbitrary message.

The NTRU decryption key includes a polynomial $f$; the encryption key is essentially $f^{-1}g$, where $g$ is a polynomial with coefficients in the set $(0, p, -p)$.  Anyone with the private key can immediately compute $f^{-1}$; while they won't be able to recover the value $g$ (that's not actually referenced within the private key), what the attacker could do is just pick a legal $g$, and then use that to encrypt any message he wants (as no one else with the decryption key will be able to determine that's not the current $g$ value. It won't be the same key as the legitimate encryptor; however it will be accepted by anyone with the decryption key.  Alternatively, he can just get any known text signed by the correct encryption key; that'll give him enough information to recover the correct $g$.

It sounds like what you want is a signature method; that is, a way where someone with the private key can 'sign' a message, and anyone with the public key can verify that signature (but cannot generate their own signatures).  There are lots of signature methods known; some proposed methods are based on NTRU, but the unbroken ones are fairly new; I'd personally wait for cryptanalytic results against them, but if you have your heart set on an NTRU-based method, you can look at this paper.  That would certainly be more secure than what you're doing now.