Linking attachment image to full sized image page instead of file (jpg, etc.)

This question is related to this thread about how the gallery attachment pages don’t display the full-size image when you select ‘Link thumbnails to: Attachment Page’ in the gallery settings dialog. Instead WP shows the medium sized image, which in turn links to the actual full sized version of the image directly (not on any sort of page) by default.

If I haven’t lost you so far, I was wondering if anyone had a strategy for linking that medium image on the attachment page to an attachment page containing the full sized image, instead of having the default link on the medium image go directly to the full sized image without an attachment page surrounding it?

Currently ‘Link thumbnails to: Attachment Page’ on the gallery settings dialog creates a link chain like this:
Gallery thumb -> Medium Image Attachment Page -> Full Sized Image File

And I’d like to do it like this:
Gallery thumb -> Medium Image Attachment Page -> Full Sized Image Attachment Page

How possible is this?