The reason for the difference in lateral positions is due to SLOP (strategic lateral offset procedures). We can fly either down the middle of the track or 1 or 2 miles right of track. The reasons we do this are:
1) to avoid wake turbulence from aircraft ahead

The turbulence must be carried sidewards by any crosswinds, right? As well as sink under its own momentum?

2) nav systems are now so accurate that an aircraft flying the wrong way would hit you absolutely head on so we all offset to the right

GOL 737-800 and a Legacy did not collide head on, cockpit to cockpit, but Legacy winglet sliced off a dangerously big part of 737 wingtip, so the 737 did not keep flying like Legacy did.

The wingspan of a Legacy is something like 0,01 miles, and that of 737 is 0,02 miles. The total height of 737 is something like 40 feet on ground, less than that in air with wheels up – Legacy is smaller, and a wing with winglet has a rather limited height. You would have to be massively unlucky, or else too accurate for your safety, in order to actually collide, rather than miss by 0,4 or 0,04 miles sidewards or 100 feet or 10 feet vertically… in the midst of the big, big sky.

3) if an aircraft overtakes or undertakes directly beneath the radio altimeters sense it as ground and can put some aircraft types into a landing mode (certainly the case on Airbus types)

If you are on different RVSM flightlevels, does it mean that the distance between overtaking planes is about 2000 feet, or multiples?