I can't see the dialog  Box that you are referring to, so I don't know how
you are attempting this. Can you post a screenshot somewhere, or describe it
in more detail?

As an exercise, I opened a site in SPD. I then copied the EditForm.aspx file
for a list  and renamed the original to EditForm_orig.aspx. I then modified
the EditForm.aspx and saved the changes. When I refresh the page in the
browser, the changes appear. Both files appear under the list in SPD, and I
can see both in the List -> Properties Dialog box  on the Supporting Files
tab. I didn't need to reset the server as these were simple CSS changes on
the page.

I tried this with "Contributor Settings" enabled and disabled, but didn't
see a difference.

Make sure that you are saving the new form  for the content type in the list  and
not for the folder content type. There is a dropdown in the supporting files
dialog box  that lists any content type in the list and also includes a listing
for folder. Since the dropdown is arranged alphabetically it defaults to folder
if the content type is something like a task or issue that comes later in the
alphabet. If you don't change that it tries to associate the form with a
folder, which can't be done. You get no error, it just doesn't work.

My approach was to rename the form  rather than change the
setting, so I didn't run into this problem.