Well, then I’d advise a plugin using the OnDocFormSave event. Have the plugin code convert the POST tvname value, then store it in a custom table, along with the document ID.
You could use the OnBeforeDocFormSave, and just convert the value, and leave it for the save process to continue to store the unixtime value in the normal way in the site_tmplvar_contentvalues table. But in this case you would need to keep in mind that this particular TV date is not stored in the normal format, and you would not be able to use the Date output widget with it.
Here’s the code MODx uses for pub_date and unpub_date, which use the same date/time picker:
list ($d, $m, $Y, $H, $M, $S) = sscanf($pub_date, "%2d-%2d-%4d %2d:%2d:%2d");
$pub_date = mktime($H, $M, $S, $m, $d, $Y);