I have the Vortex Viper HSLR 6-24 x 50mm (30mm tube) FFP in Leupold PRW Med rings = .097″… mounted to the exact same rail and it fits perfect. You should have about 1/8″ – 1/4″ clearance from the barrel to the front objective bell with the rings you mentioned depending on forward or back location, you have room to adjust before the bottom taper on the scope contacts the rail if you need to bring the scope back toward you.
I'll take a picture of my setup tonight and post a picture so you have a good reference. The Vortex and the Sightron S3 should be very similar in size.
Just so you know the rail on the 300wsm Lite is a 20moa rail…hopefully this gives you a good idea of how the 20moa and 0moa rails look with a 30mm tube / 50mm objective.
The rail on the Varmint is cut to receiver length. I didn't care for how it hung out over the barrel so I cut and shaped the front with a round profile to match the receiver. Its a aluminum so a little matte black paint and you would think it factory. I'll be doing this with the 300wsm rail as well when i have a chance. I prefer the look and length of the Tac and Super Varmint factory rails.