Generally "off-the-shelf scripts" never turn out to be exactly what you want, at least for me. Since this isn't too difficult to make, I would create my own. Here's a nice thread on Basics of Submitting and Emailing Forms with PHP [webmasterworld.com]. This tutorial uses mail [us3.php.net] however another good alternative is using PEAR::mail [pear.php.net].
I had a similar problem. The bounces stated that the domain names for the email addresses were unroutable. It turned out that my host had set a maximum of 1000 emails per hosting account per hour. They kindly agreed to remove the limit.