20mm is plenty of room for a leaf shutter.
Your friend is going to have to learn how flash works, or invest $10,000's in high end strobes. Most strobes duration at decent power outputs is in the sub 1/500 sec range, so sync speeds faster than that become 'interesting' to actually use. At very high shutter speeds the leaf shutter works as a second aperture diaphragm too.
Global shutters with very fast read speeds are the answer for the future for high speed sync, but even they don't overcome the flash duration issues.