From what is described, it seems the routing in these routers is marking everything for a given destination and the routing tables are assigning it a single WAN. It's all most likely just some linux with iptables and iproute2 installed. Since connections are marked just once with iptables if you are reusing the connection it will always go out on the same route. It does sound like the firmware is a bit flakey in this regard.
But then thinking about it, if winamp is not trying to download with multiple connections but just one then ofcourse it will only go as fast as one of the connected lines. Since iptables will handle that one connection, the routing for everything on that connection will go the same way. Trying to split up the content of a single connection across multiple WAN lines each with a different IP might just be a total nightmare. For one, the server on the other side is not going to send a packet to an IP different from the requesting one.
Just curious though, but why 3x 1MBit lines when a 4Mbit will do?