Fix timestamp parser in new load_stats_file.

The previous parser only considered stats files _starting_ with the
timestamp tag, not stats files having the timestamp tag in a later
position. While this applies to all current stats files, a future
stats file might look differently. Better to fix the function now than
be surprised in another 9 years from now.

This commit also adds a test case for such future stats, and it fixes
stats file paths in newly added unit tests.