No, rekeying does not solve that problem, not to mention which you've just handwaved a hard problem (varying the key over different sectors). That's doable (though it again doesn't fix the problem with your proposal), but the resulting mode isn't CTR.
This is a sequence of non-sequiturs, none of which respond to my comment. I'll make it easier for you:
Propose a scheme whereby you use AES-CTR to encrypt a 100 megabyte disk of 512-byte sectors, whereby the scheme "rekeys" every "few sectors". Be specific.