OK, I think I ruled out the block-level copy step as a possible problem. I just successfully restored the supposedly problematic-backup to a different 2008 R2 server in the remote data center.
One item of interest, in the error log I see hundreds of thousands of the same error message that returned when the backup fails:
RESTORE detected an error on page (0:0) in database "database_name" as read from the backup set.
Error: 3183, Severity: 16, State: 1.
Many thousands are entered with the same time stamp, and then many more thousands a second or two later.
There are no special teachers of virtue, because virtue is taught by the whole community.
--Plato