Improving EC2 ping times from home

Slightly strange one this, and maybe not SO appropriate, but I know you guys will have the answer if there is one.

I've been trying to run a gaming machine in EC2 following the excellent blog post by Larry Land here. The problem I have is latency from my home to my nearest AWS region. I get a ping of around 35ms, and I'm looking to improve on that. Is there anything I can do? I'm using Steam n-home streaming over a Hamachi VPN, on Windows Server 2012.

My internet connection is roughly 120Mbps down and 35Mbps up, and there's nothing I can do to improve on that sadly.