SSH rekey security implications
I think you overlooked some words in section 9:


  Key re-exchange is performed using whatever encryption was in effect
     when the exchange was started.  Encryption, compression, and MAC
     methods are not changed before a new SSH_MSG_NEWKEYS is sent after
     the key exchange (as in the initial key exchange).


Note that it is better to keep to the naming of the methods within the protocol, i.e. use key re-exchange instead of re-keying. That makes searching and conversation much easier...