For replacing the crontab file, I would use the crontab command:

...
open(OUT, "|/usr/bin/crontab -u USER -")
  or die "open: $!";
print OUT ...new crontab contents...;
close(OUT);
[download]

See man 1 crontab for more details. This ensures that the file is safely replaced and that the cron daemon is notified of the change.

Unfortunately, you still might have a permissions problem if your web server is not running as USER.