The SL2 and R6.2 are wonderful cameras by all reports, although I can't report from first-hand experience. I'd love to have either one. I thought Sean might be price sensitive, and that's where the R3 has the advantage. The SL2 and R6.2 are rarer and much more expensive used, whereas the R3 sold very well, and is readily available used. You can check the usual suspects for prices. My recollection is that a clean R3 is in the $250 to $300 range, and both the others are in the $1000+ range in very good or better condition.
I don't have the actual numbers on the shutter lag times for the R3 and R4s, but the difference is very noticeable to me in use. As I mentioned earlier, there appears to be much less difference when the R4s release is already held halfway depressed (to the exposure lock point). The Sept '78 catalog I have mentions the short "time parallax" on the R3 as a feature, but doesn't give numbers. Given its mechanical shutter, I'd expect the R6.2 to be faster.
I shoot soccer myself, but for that I use rangefinders with 1:1 built-in (Bessa R3A) or auxiliary hot shoe mounted finders. On the Bessa T, R2, and R3A I have to consciously delay my shot so that the struck ball is leaving the foot as it follows through to imply action. Otherwise, if I press the shutter button at the moment of impact, I get a foot that on close inspection is putting a 2 inch dimple in what looks like a static ball on the ground. I use a 135mm Hektor (readily available in VG condition for $99) outdoors and a 75mm CV Color Heliar indoors. The 1:1 brightline finder is tremendous for sports. With both eyes open you can still see the whole field, watch the whole game with camera "at the ready", and anticipate action coming into the frame.
If anyone has data on shutter lag times for the SL and R series, I'd be interested in seeing them.