Looks like there are several options:
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mysqldump + rsync – can this be done for only specific data from an existing table, and not a whole table?
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An insert to a federated table – this seems pretty untested and unknown at this point…
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A Python script (pull into memory from A, then insert into B) – this would probably be pretty slow…
What kind of data warrants what method?
You also have another option — mysql replication!
Can you not extract that single table into its own database and replicate just that to the second server (or as many servers as you like)?