Perl's time() function and MySQL's UNIX_TIMESTAMP() function seem to have completely different ideas about what time it is

Actually, they don't. The epoch from where time is calculated is January 1, 1970 for both MySQL and Perl, unless you happen to use a Mac OS, where the epoch is January 1, 1904.

$ perl -e 'print time(), "\n";' ; mysql -e "select unix_timestamp()"
1053097150
+------------------+
| unix_timestamp() |
+------------------+
|       1053097150 |
+------------------+
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See also Perl's time and MySQL's timestamp for more about this issue.

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