Just from your description it sounds like your float level is too low.
I have had experience with the PJ and the PWM Keihin carburators. They will run just fine while puking fuel out from a high float level. Your competitors may not like you though!
The PJ needed the inlet needle and seat changed (machined out and replaced) to work properly on a RR track. Even then, the float level was extremely critical and very sensitive when it came to cornering at any speed.
The PWM is far more user friendly. Pump/fuel line set-up is straight forward too. (see below)
If you are using a round Mikuni pump with dual outlets I would suggest running one line straight to your carb, and the other as an unrestricted return back to your tank. This is a standard starting set up. (50/50) *** -> Pulse line as short as possible!
Set your floats (bowl off, carb upside down) so the fuel shuts off when the float seam is just past that seal/gasket surface on the carb body. This will be a little on the high side but a safe starting point. This is easy to do, put a piece of fuel line on the carb, turn it upside down, blow into fuel line and work the float arm with your finger, finding the point where the fuel (air) will shut off. Do it a few times and adjust it to be just beyond view hidden by the carb body at that gasket surface.
Float level on the Keihin is crucial and will change transporting your kart to and from the track. Once you get it right you may not have to check or adjust it everytime but it is something you will have to manage. I would keep multiple float arm assemblies preset to different levels and just swap them out instead of adjusting them all the time.
I am not an advocate of the “pump around”, never used one and never really needed to. It just takes some testing to figure out the fuel line configuration that suit your fuel system. Not sure you will get that PJ to work consistantly on a RR track but I wish you the best of luck!
Can’t believe there were over 130 views and no one bothered to throw something at you here. Not sure where you are located but we are testing all day at Grattan Raceway in Western MI April 8th if you want to work it out. Plenty of CIK shifter guys will be there to assist you.