I had to come up with something similar to handle a master "Template" folder that I copied: each copy had to link to the *relative* page in its hierarchy, so the normal MODx link syntax didn’t work because it links to an absolute URL as you noted.
The solution was a bit ugly, but it worked: it involved using the Ultimate Parent snippet and an output filter:
<a href="[[~[[!UltimateParent? &topLevel=`3`]]]][[~207:stripString=`[[~113]]`]]">Relative Link</a>
In the above example page 113 was the parent folder, and 207 was the target page in the hierarchy. This let me copy something like:
www.mysite.com/some-folder/somepage
And end up with links to
www.mysite.com/copied-folder/somepage