You could separate the content from the web part, so that you can use a content-only page type to store the content, including the multiple attachments field. The web part properties would simply allow picking the content, or filtering the content, to be displayed.
I'd suggest separating the content from the web part anyway. This allows changing how the content is displayed, and using it multiple places, without requiring authors to reenter the content. Theoretically, the content could survive a page redesign.
Check out Brenden's answer to this old post. It'll probably get the ideas flowing.