Fix publish step failing when multiple recordings processed in one run

The logic for deleting the process done files was wrong, resulting in
the script (attempting and failing) deleting all of the done files for
all of the processed recordings after the publish completes for one of
them.

Fix the logic to only delete the process done file for the recording that
just completed publishing.
Merge pull request #405 from kepstin/recording-updates

Fix publish step failing when multiple recordings processed in one run