Did your controller have field weakening (or over speed) before?
If not you might want to increase your turns back up to 5 turns
If you want around 3000 RPM maximum and plan on using field weakening controller, like the Sevcon Gen4, I would target spinning 2500 No-load without field weakening, if you are planing on running the Sevcon Gen4, the max nominal voltage you will have is 104V, and you want to run that if you want the best performance out of that controller, so I would target 2500RPM/104V is about 24RPM/V or only about 2.4x the KV of the original Motor.
To follow your original math, you had 31 turns, and you doubled the thickness of the stator so you would need 15.5 turns to get the same KV, you want 3x the kv so 5turns, then switching to Wye decreases by 1.73x which would end up with 1.8x the Kv of the original Motor
4 turns WYE shoudl give 2.2x the Kv of the original Motor
3turns WYE should give 3x the Kv of the original Motor.
Based on that I woudl go with 4 turns.
Lets look a the torque numbers though and see what you really want
In other threads you can find that Kt (Nm / A) is equal to 9.549/kv , so a 4 turn WYE,double wide motor with 2.2x the original KV would in theory have 22RPM/V = 0.434Nm / A. I know that RMS amps and DC Volts and stuff are all confusing, but from what I have experianced that conversion works pretty good at predicting Torque / Phase RMS apms as reported by a Sevcon controller. So a Size2 with 250RMS phase amp limit gives 108Nm of torque. With a 20" OD rear tire, you would get about 120kph at 2000 RPM, which sounds about right, maybe a little high for most of the kart tracks and be fun on the road. So you would want a 2:3 ratio on your gearing so 3000 motor RPM = 2000 Wheel RPM, that would multiply your torque at your rear wheel by 3/2, so rear wheel torque is 150Nm. With a 20" OD tire 10"radius (0.254m) that woudl be 590N of force to the ground .. 590N is about 130pounds force. I imagine you and your bike will weight something like 260lbs all up, so that would only give you about 0.5G acceleration. at 1/2G acceleartion your theoretical 0-60 time is around 5.5Seconds, which isn't bad, but it won't make you crap your pants which I think is what you are going for. To do that you would need to upgrade to a larger controller, or go to more turns, maybe 5, and sacrifice power available at top speed, or gear a little shorter which would be easier on your motor / controller, but would certainly limit your top speed.
All this math was done quickly so I could surely have made a mistake .. please check it over and tell me what you think.