Yes, you are correct this approach would be vulnerable to a simple man-in-the-middle attack. Just sniff packet headers to find out what port the server is accepting indicated by packets sent back with an ACK flag set. Headers with that flag set will be the currently valid port at that instant, since all other packets will be sent back with RST set (blocked).

And yes you could have potentially very frustrating synchronization problems. With TCP you wont be able to control certain things such if a connection request is going through exponential back-off due to network congestion. For example, lets say you could make a connection request within your alloted tolerance, but if there is network congestion and your NIC is not getting either RST or ACK packets back, it will continue to send connection requests at continuously increasing intervals which you cannot easily control since its done at the transport layer. Then one of your connection request packets finally reaches the server late, and you are blocked from connecting again for 15 minutes.

If you could work around the second issue though it could work. I think its a great idea in general, nice creative work!!