The stumble/backfire on hard acceleration is caused by not enough accelerator pump "shot". In other words on hard acceleration the engine gets a gulp of air before it gets fuel. This results in a lean condition and the engine will stumble or backfire. The accelerator pump is suppose to supply extra fuel on hard acceleration to eliminate the lean condition.

With the engine SHUT OFF, look down into the carb throat then open the throttle quickly. You should see a solid squirt of fuel.
Sometimes you can adjust the carb linkage to increase the pump
"shot".

Let us know what you find.

Ron