[ford38v8]

Sloppy bushings shouldn't cause a stumble, unless the shaft hangs up. More likely, the accelerator pump piston is of a poor quality, or even the shaft is wrong, as kits do come with multiple parts for different carbs. You'll be much better off with a soft leather piston soaked in oil. The kits these days usually come with a funky blue material that doesn't hold up to Ethanol.

Another likely cause of the stumble would be the size of the main jets. You need .051 jets for a single carburetor. Smaller jets are used with multi carb setups.

Other than those two causes, there can be obstructed passages, missing or stuck accelerator valve ball, ineffective power valve (AKA Economizer valve), vacuum leaks, or any number of combined ailments.

You can get a good kit and any parts you need from Daytona in Florida. Not cheap, but you get quality parts.

Daytona Parts Co. daytonaparts.com/index.html
World Class Carburetor Restorations and Carburetor Kits