I was thinking the same, but you'd have to figure out how to create the VPN to the EC2 instance for multicast forwarding, since presumably the Steam Link won't be able to run OpenVPN.
Add another piece of hardware. Cheap off-the-shelf Linux-running hardware. A rebadged Netgear router that'll run OpenWRT is £7. Worst case, Raspberry Pi is £45 including case, cheap small SD card, PSU and an extra USB Ethernet adapter.
