I'm not sure why those companies would have issues mitigating those attacks.
I curently have a dedicated box with OVH and we have received the same attacks as you:
Random src port
Random src ip
Teamspeak dst port
Teamspeak dst ip
They had no issue mitigating the attacks and we experienced very little to no latency increase with no reported user issues. This is also with no configuration of any firewall rules in the OVH panel. I believe their gaming server packages offer different DDOS protection (ie. Layer 7 protection) over their standard dedicated server packages and they list Teamspeak as one of their officially supported applications.
You may have tried this same solution, I am just giving you my personal experience with this issue.