Quantum Secure Signing Algorithm with a 256 bit signature & key. Am I missing anything? Can I remove tradeoff?
In most cases, multiphases is fine. After all, Lamport is essentially multiphase.. send public key, send signature.


Not quite - with Lamport (or any other signature scheme), after seeing the public key and the signature, an attacker still cannot forge a signature; with your technique, he can.  Almost all uses of signatures rely on this property, and so your technique cannot be considered a general replacement.

If what you have meets the requirements of your problem space, that's fine.  Just realize that it really is a niche solution...

Actually, if you're happy with the limitations of your method, it can be simplified somewhat: to "sign" a message $M$, pick a random string $R$, and transmit $H(R, M)$ and $M$.  Then, in phase 2, transmit $R$.  This uses one fewer hash (and the hash can be of shorter length, as we're not giving away half the bits in the commit phase).