@ chris0 - I briefly had some Mavic mtb shoes where the tread interfered with the ATAC cleat. I think it was a tread depth issue, as fitting a shim between cleat and sole (about 1 or 2mm) solved the problem.
You could just scrape/slice/hack off a bit off the top of the tread on the lugs to the left and right of the widest part of the cleat.
Never had this problem with Sidis.
I've done a google search but can't seem to find shims for time cleats. Where did you get yours?