Website contact forms often send 'from' the website, so tickets will be created 'to' the website. In order to use the 'reply-to' address follow this thread to make the changes needed for IMAP or POP3 http://osticket.com/forums/showthread.php?t=497(http://osticket.com/forums/showthread.php?t=497)
But you still like the idea of piping emails back and forth for its quickness factor.
So...
Enable both POP3/IMAP fetching and Email Piping in osTicket. Do the setup. You'll need to setup your email piping on your control panel too, and you'll need to set a cron job for fetching by POP3/IMAP. I've set ours at 5 minutes intervals.
1. Set up a department (eg Support) and set up your piping email address to associate with that department, and use that email as your default sending address for that department.
2. Set up another email address that is associated to the same department, and this will be the email that is checked via IMAP/POP3.
3. Set your contact forms to send to the IMAP/POP3 email address in #2.
This way your osTicket will poll for new emails from your contact form every few minutes, and use the reply to address to create the ticket for. All further correspondence sends from your piping address, and customers respond to the piping address, so everything is very quick, and you do not need to wait for your cron job to catch up.
When somebody uses your piping email address in the first place, the 'from' field is used from the header, as is the name field, and the tickets are created instantaneously.
Hope this helps someone.