No, moving to linux would not help much, if at all. Distro shouldn’t matter much.
With linux (or anything else that supports traffic shaping and fair queuing) you can improve performance at high network load, but this will only be a big gain if there is non-game traffic that you can put at a lower priority. It will also work better if the traffic control is on a box between the server and the internet, rather than on the server itself (allowing you to actually shape both directions).
See http://www.lartc.org/
and in specific: http://lartc.org/howto/lartc.cookbook.ultimate-tc.html#AEN2210
ISPs know that they are benchmarked solely on how fast people can download. Besides available bandwidth, download speed is influenced heavily by packet loss, which seriously hampers TCP/IP performance. Large queues can help prevent packet loss, and speed up downloads. So ISPs configure large queues.
These large queues however damage interactivity. A keystroke must first travel the upstream queue, which may be seconds (!) long and go to your remote host. It is then displayed, which leads to a packet coming back, which must then traverse the downstream queue, located at your ISP, before it appears on your screen.
You may be able to get a plan from your ISP with more upload. Mine offers up to 600kbit up on DSL.