The step you're missing is the one that tells Outlook to use the custom form as the reply form. That actually takes two operations -- one involving a custom form and one involving an Exchange event sink or some other operation to make changes to the items in the folder.

In order for Outlook to use a custom form for replies, the Reply action on the original item's form needs to be set to the custom reply form. This means that the original item itself needs to be using a custom form. This can be a separate form or possibly the same as the reply form, depending on the application. The important thing is that the Reply action on the form's (Properties) dialog must be set to the custom form you want to use to reply ... and that in turn means that the reply form must be published not to the public folder but to the Organizational Forms library.

As for the form for the original messages, it can be published to the public folder, but you'll still need an event sink or other application to alter the MessageClass property on the items in the folder.

All of which is a long way toward saying that you'll need to cooperation of your Exchange administrator to make this work.