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Sure does seem to be missing from the obvious places, doesn't it? Probably because it's not actually in a menu anywhere.
Recording an action does yield a bit of a clue... It records as Merge Visible With Duplicate:
The Alt seems to add the "With Duplicate".
Just a guess, but based on the above, if you were to change the Merge Visible shortcut to something besides Control-Shift-E you might find that adding Alt to whatever you assign to that function would be a Stamp Visible operation. I didn't try that.
Or you could record an action as above and assign it a function key.
thanks a bunch, yeah I did try to remap the shortcut and then just add ALT to it, but that didn't work.
I'll probably just record the action.