If you really want the Lego studs to work, you could always epoxy some genuine bricks to the printed stand. Many of the dimension / tolerance issues arise from the slight interference fit necessary for removable parts - it looks as though this would only be required where the figures fit the stand?
Yes, only uses the studs for the minifigures, taking your idea a step further I wonder if I could design a small lips which would hold a 2x2 lego plate, avoiding the need for glue.
If you really want the Lego studs to work, you could always epoxy some genuine bricks to the printed stand. Many of the dimension / tolerance issues arise from the slight interference fit necessary for removable parts - it looks as though this would only be required where the figures fit the stand?