I would check out the main culprits. Check them all out, and fix them all otherwise you may be chasing your tail for a long time.
1 rebuild carb with Genuine Mikuni parts only! Replace needle and sear with genuine Mikuni Viton type Needle.
2. Replace all gray lines with automotive fuel lines. 1/4 and 5/16 for the 951 I believe.
3. Replace fuel selector switch
4. Replace fuel filter (water separator) gasket and filter
5. Check for leak in the pulse line going from the bottom of the engine to the rave solenoid. It could have a leak and cause it to run lean. Mine was totally ruptured.
6. Replace the carb base gasket when you reinstall carbs. I have heard to never reuse a carb gasket.
Also check the oil lines and oil filter. They need to be replaced periodically.
Some of the guys on here have a troubleshooting method to determine if it is a leak from the fuel system. They recommend running the fuel line directly from the reserve nipple to the carb. If your problem goes away, then you know it is in the selector/separator area. I just replaced everything and pressure tested mine like the manual says.
I don’t think your accelerator pump would be causing it to run lean. It just dumps a little fuel in when you hit the throttle. But I am not an expert. The manual has a procedure to test the pump. I tested mine and it was working ok. Just needs to hold pressure for a little while. Also a check valve test if my memory serves.
Finally, if it is a stock ski, make sure you are using the stock low speed and high speed adjuster settings. Should run well at those settings.
Hope you find out the cause. Good luck!
Ken