CSRF-Protector-PHP | CSRF Protector library : standalone library | Hacking library

The answer to your original question is quite simply no, I'm afraid. You do not have sufficient control over the connections to enforce anything. As you write in your edit, setting the cookies is done via headers and this happens asynchronously.

Regarding your edited question: you can make this work by storing multiple tokens per client. That is, every time a new request comes in from a client, don't delete the current token, but only create a new one. The client side should then not only send the correct token, but also the correct "connection ID". This ID can simply be a counter for number of requests from a client.

Alternatively, you can opt to not refresh the token for AJAX requests, but only for normal page loads. Depending on how your site works, this may not be safe though.