Since the signatures all generate the public keys, those can be derived from sig and proven by pre-commited XOR of every pub key compared with XOR of every signature end hash.
If I understand you correctly, you're proposing that we have a number of one-time-signatures (which, with the corresponding messages, hash to the corresponding public keys), and then we produce the xor of all the public keys. Then, the receiver would validate all those signatures together (by computing the corresponding public keys, xor them together, and seeing if the result is the published xor).
If so, it doesn't work; an adversary could put together a forgery, that is, a series of messages and signatures that would evaluate to that same xor. How he would do so is straight-forward; he would generate a series of messages and random signatures; he would then find the corresponding public keys. Then, he would find a subset of those public keys that would xor to the published value - this can be done by solving a set of linear equations. That subset would be the forgery.