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*crickets*
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The good news is that I've figured out what the problem is 
The .vmdk file listed several extents that were simply missing on disk, and apparently the way VM Player responds to this situation is silent failure. Nothing even in the logs about it.
I figured this out by installing VMWare Workstation using a trial license. When I tried adding the .vmdk to the VM it responded with the error message "the system could not find the file specified" which, while only marginally more helpful than silence, allowed me to track the problem down to a missing extent.
It'd be nice if someone at VMWare improved the error behaviour a bit.