Interesting.
So the traces are proving you're at least making it to the border router between Verizon and Limelight Networks, but you're also getting at least one hop beyond a Verizon controlled router. The traffic is staying within the US, so that's a plus. In addition, it's dumping off of Verizon rather close to you in a grand scheme of things. Afterwards the traces time out, so is it a question of the endpoint not accepting UDP Echo (default for *nix systems), or is it a question of a range being filtered outward.
I would try running Wireshark against the LG player or at minimum, see if you can get a dump of the NAT Table for your router which should show the destination, since if Verizon was manipulating the route on the fly by simply sending data to another place (rather than redirect via HTTP/DNS) you'd likely not be able to communicate at all with Vudu. If you have equipment capable of doing a man-in-the-middle capture, such as a switch with port mirroring, a hub, or a Wi-Fi adapter capable of capturing traffic, I'm curious if the Blu-Ray player is getting a particular response back from Vudu or if it's a case of just not getting a route. Assuming the traffic is not encrypted I suspect it should be easy to get.
I'm honestly not sure what Vudu is trying to accomplish blocking proxies and VPNs, though. I feel like they're shafting more than just the foreigners. VPNs and Proxies come in so many forms it's nearly impossible to filter them out without breaking things for others.
I would also consider checking the WHOIS record history for your Public IP address from Verizon. I know in recent months folks have been having on and off issues with getting to services due to Verizon assigning out freshly allocated IP addresses. Some of them came from other providers, for example that were not within the US. It's also noteworthy to point out that many folks run Tor exit nodes on FiOS. I don't know if they run them off of Dynamic IP accounts, but since you can switch between Exit nodes, that's something to consider.