[Formulajones]

Usually when you have a brief stumble or lean spot off idle before the main circuit takes over as you described, it either the pump circuit or the power valve circuit.

If you increased main jet and it helped it's likely covering up the issue you can accomplish the same with the idle circuit as well by richening that. Typically not the best approach but some engines also don't like lean mains or lean idle circuits either. It's a game of back and forth.

If youve messed with the pump circuit with no improvement then the other likely cause could just be too much of a delay in the power valve circuit. It has to work in conjunction with the pump shot. The pump shot alone won't always cover the lean spot when the throttle cracks open. That momentarily drop in vacuum should also trigger the power valve circuit if for only a second.
You may just need to change the power piston spring.