I have the same problem with 17 HP intek. Have done the same things you have with no results. I also have to prime it regularly on initial start up from storage. IMO cheaper briggs engines have about three design problems. this is just one of them along with the compression release system and the air filter design. This IMO puts intek in the Low end engine choices when I buy new produce. I been mechanic for 45 years was was Quadra Jet and autolite carb. master at one time.

Have you checked that the throttle cable is adjusted so the choke is actually closing all the way? IF so, I would think about blocking off one or two of the holes drilled in the choke butterfly. I have not had that problem with Intek engines and I have rebuilt a lot of them. The carbs are not made by B&S by the way. Two brands are used.

Nothing wrong with the compression release, read your owner's manual.

Air cleaner design was a problem with the earlier ones, they have an excellent air cleaner system now.

Walt Conner