Thanks for the helpful responses.
It could be modified to draw from multiple places to reduce the need for underfloor flow. Also consider ventilating more with a HRV or pressurizing the basement (vs depressurizing underneath the slab).
The basement is round 23'x23' and the current system draws from two points located against the outer walls at basement midline. It uses 3" pvc connected to an RP145 fan. It's rated for 166 cfm at 0". I don't know what the actualy system pressure is. I've considered an HRV to further dilute the radon, but would also like to make sure I make the most of the currently installed system.
Bob I:
In addition, I'm unclear if your planned french drain will be sealed from the living area but it needs to be. The right way to do this is, as you said, remove the slab, excavate some amount including a deeper drainage trench, install washed stone, a drain or sump pump, insulation (2" Styrofoam or EPS), a heavy, taped, poly vapor barrier which runs up and is fastened to the walls & then a concrete slab. Add a loop of 4" drainage pipe which will tie into the radon vent, then pour your concrete. Should be much lower level after all that.
I think a partial short circuit of the subslab vacuum is occurring because there are a few places where the perimeter backer rod was placed between the wall bottom plate and the foundation wall, and not between the slab and foundation wall. This is a relatively small portion of the perimeter (maybe 10 ft?), but I'm not sure how much it's contributing. The planned french drain would be placed next to the footer and include dimple mat about one foot up the wall. It will be sealed and the walls eventually insulated with EPS that is sealed at the floor junction and the top of the wall. The french drain should improved air flow under the slab, and sealing it as described should be an improvement over the current state. My fear is that we go through all that trouble (french drain only), and it's still elevated. Replacing the slab as you describe sounds more reliable, but also significantly more expensive. Is there a way to estimate costs for replacing the entire slab and laying new stone? Is that done by a waterproofing contractor?
As jonr mentioned, the dimple mat bathtub would handle limited moisture. But shouldn't this accomplish air tightness similar to the approach outlined above? I'm not sure I can insert a link, but there's a similar description at the site below. It was also described on the Buliding Science website, using closed cell foam instead of dimple mat on the walls.
http://aarst.org/2014/1_Freeman_SOLVING-THE-CONFLICT-BETWEEN-BASEMENT-WATERPROOFING-BEST-PRACTICE-AND-RADON-MANAGEMENT-IN-THE-UNITED-KINGDOM.pdf
The walls of the basement are damp about one foot above the floor. I'm not sure how much moisture the dimple mat system can handle. We don't plan on finishing the basement, but would like to insulate.
I appreciate the help.