Would UDP and something like bittorrent help?
Changing to UDP would get rid of the congestion control but UDP on its own would have congestion issues killing its throughput.
Bittorrent created their own congestion control called ledbat and then added that onto UDP to create UTP which could help. There is also UDT which has its own congestion control algorithm designed for 10gbps+ connections, which would significantly fix the issue.