Key the rotary table to the table. You can accomplish this with dowels or actual keys. This provides the most positive resistance to bumping the rotary table out of position with a milling cutter taking greedy bites out of your part as it enters the cut.
Strap clamps clamping two smooth surfaces together do not gain much increase in friction from the point of being "tight" to "bust-a-nut tight" You would be better to add more clamps or, add a friction increasing substance between the two surfaces. You can thoroughly degrease the surfaces to begin with, but a sheet of wet-or-dry sandpaper might also do the task without too much damage to the surfaces.