So, it's a year out and the EGR codes have remained gone. The EGR valves (both the old ones and the new replacement) all tested fine... the root cause must have been that cracked hose which was causing the bad reading. Make sure all your hoses are secure and not cracked. Specifically, the one that cracked for me was one attached to the lower portion of the right-hand (driver's) side of the intake manifold. I repaired it with a 2ยข zip tie.
If you have a problem that doesn't go away after replacing the EGR valve and cleaning the tubes, then use this troubleshooting guide:
https://docs.google.com/document/d/1...CvhzSrsJzmSeQ/
...if everything checks out as per that guide, it MUST be a problem elsewhere, like the cracked hose I found.
The moral of this story is if you get an EGR code, it might not be your valve. It might not even be the input and output tubes for the EGR valve. It might be a hose leak elsewhere in the system, be SURE your hoses are in good shape.