so I would guess the wider the spacing between the objectives the more pronounced the effect
Yes, and this is why porro prism binoculars have a more "3D" effect than roof prism models. The objective lenses are much further apart.
Of course, this is how a rangefinder camera works. The farther apart the RF windows, the more accurate the focus (in general.) Take a look at antique military optical rangefinders to see the extreme end.