As of v1.50, my SOUP user script now contains an implementation of this feature.
The way I implemented it is by detecting the presence of the bounty notice on the page and, if it's there, disabling all the radio buttons in the close popup that don't open a submenu. This should make the dialog obviously and visibly non-functional (and also impossible to submit, since you can't actually select a close reason), while still preserving the other functionality of the popup (i.e. checking to see which reasons earlier close voters have picked).
There's also a bit of extra code for handling the close-as-duplicate subdialog, allowing you to search for potential duplicates and to see which duplicates others have picked, but not to actually select and submit one.
Of course, there's also a conspicuous explanatory message:
(The freehand arrow in the screenshot is probably redundant. To do: Localize the message into languages other than English.)
In some later version of SOUP, I may consider replacing the current implementation with one that leaves the radio buttons enabled but instead "super-disables" the submit button, since I did actually end up adding such a feature to SOUP for another feature request. But for now, the current implementation seems to work fine. (Any reports of unexpected side effects are, of course, welcome!)