Float level sounds like a good start. Easy way to test is simply rev the motor while looking down the throat of the carb with an LED flashlight (LEDs make the gas much easier to see than using incandescent light). Hold the revs for a few minutes and see if you can empty the carb fuel bowl.
Also test the accelerator pump circuit. Take off the air cleaner, shine the light down the carb and actuate the accelerator from idle to full open. You should see a nice, solid stream of fuel.
"The usual complaint when the accelerating pump circuit goes bad or becomes defective, is a noticeable "flat spot" when trying to start from a complete standstill or a hesitation on acceleration. A quick check can be made as follows: With the engine stopped, remove the air filter. Look down inside throat of the carburetor. Open throttle by hand, slowly at first and then quickly. Watch for stream of gas coming from pump jet. It should be a steady full stream from the start to finish of throttle travel. If the stream of gas is not full and steady, remove the carburetor and completely check pump circuit."
"professionally rebuilt" does not mean as much as it used to.
