I don't think you will be anywhere near 5 lbf per CIM with a slow fly prop, although I'd love to be wrong about this.
For reference, A Draganflyer X6 Helicopter has 3 sets of 16inch/15inch contra-rotating blades, i.e. 6 blades operating at 2000 RPM at hover with a maximum gross weight of 3.3 lbs (and max power for its 6 motors of 450 watts total. So if you can beat this by 50% with a single smaller prop they will probably have a job waiting for you
The mechanical power you can get from the CIM operating from 40 - 50 amps is about 125 - 185W. But you can get that only with a torque load of 100 - 125 oz-in. You need a prop that will give you that torque load at 3800 to 3300 RPM respectively.
Slow fly props do have higher loads than normal props but I suspect that a 12 x 3.8 is still pretty far from the sweet spot on a CIM. A normal clark airfoil type prop is only going to give you about 1.2 - 1.5 lbf at 5000 RPM.
BTW, a traditional 15 x 3.8 prop at 2000 RPM would produce about .61 lbf. So 6 of them is within 10% of the max gross of the X6. Drop the prop to 12 inches and you've got a quarter pounder.
I've seen test data showing an APC 10x3.8 slow fly turning at 6850 RPM producing 1.54 lbf static thrust which is pretty good agreement with 1.69 lbf for a normal prop. Note that this is already above the max recommended speed. Slow fly props are not as sturdy as conventional props. You won't get the CIM anywhere near 6850. I think you'll see 1 - 1.5 lbf.
I think the major difference in the slow fly is that you will have better performance at slower speed but nowhere near the improvement of dropping the pitch under 2.
Once the robot gets moving, the effective pitch drops and the slow fly should increase faster to its max thrust point. The normal prop will never get to that point. The lower pitch prop is starting out well ahead of the slow fly and will also improve.
It should be interesting to see what end's up working out the best and what can survive the abnormal precession forces resulting from robot collisions. This is unexplored territory.