This isn't an original observation: I got it from one of Chris Schwarz's "workbenches" books, and/or one of his blogs.
My suggested work-around to this problem -- although non-traditional! -- would be to cut a series of vertically-oriented rectangles in the apron. This would allow clamping access.
The top end of the rectangular holes would not be flush with the underside of the surface of the benchtop, but would instead be perhaps a half inch or three-fourths of an inch of remaining material (i.e. running "with the grain") hanging down below the underside of the workbench. (The specific amount would depend on the configuration of your clamps.). You would then clamp **through** this access hole, to the underside of the benchtop.
I've tried out this approach on my own workbench -- and it seems to work.
Please see the photo below -- which is a poor but illustrative sketch overlaid on an outdated photo. Specifically, the little black rectangles across the front of the workbench.