The method described should work for you as long as you have browsed to the correct downloads folder on D. But if you find it easier you can always set it to Always ask me where to save files and then select the folder on D as your choice.
The desktop shortcut is nothing to do with where you download - it is simply a means of you accessing the folder on D.
I even changed the name to cut confusion it's now called newdownloads.
and shows it that way in FF options. but downloads still go to c user user downloads.
The older I get I find I know less and less about computing I have been in the business for awhile started in 1969.