Thanks to a tip from Richard Eriksson, I've completed the Movable Type utility to close comments and trackback on all weblog entries after they become a week old. I will be releasing it tomorrow under the GPL, assuming it runs properly as a cronjob and closes these seven-day-old entries to new feedback.
I couldn't get the script to work until I used Timothy Appnel's mt-rebuild utility to republish individual entries after they have been closed.
I run mt-rebuild from PHP with the language's system function:
system("$this->perl_path $this->mt_rebuild_path -mode="entry" -blog_id=$entry_blog_id -entry_id=$entry_id");
The $this->perl_path and $this->mt_rebuild_path references are object variables that hold the locations of Perl and mt-rebuild.