I don't understand how your proposal would prevent pool mining.

The pool creates the header, puts their address in there, and sign it.  Then they send it out to the "miners" to search for the hash.

When a "miner" solves the block, the pool broadcasts the block and gets paid.  Then in a later block, they split up the payment among all the participants.

What am I missing?  Is there something implied in your description that I didn't notice?