I took it apart to find out which controller it has (it's a WK3612YS), but I couldn't find any information on programming that.
I then trawled the internet for any general ebike speed limit information. I stumbled upon "the mad Rumanian", who on a completely different ebike, disconnected the short white wire that comes out of the controller and goes back into it, and that removed his speed limit, so I searched for the same on my S6.
Not quite the same on the onebot S6. I found a short (10cm) black wire and a short white wire - neither of them were connected to anything, but one had a male and the other a female connector on the end. I took a gamble and connected them together. Hey presto, a slightly faster S6!
I then tried various combinations of the three P3 settings - I don't know exactly what they control, but by changing them you can vary the initial pull away torque and the highest speed.
I found the best compromise to be as follows:
P3-1 = 3
P3-2 = 6
P3-3 = 7