Most stealerships are useless you're biuying something.. Then you have their undivided attention..
I'm not a sporty guy, but I wrench on most ALL Hd's.
The new bikes come super-lean to pass EPA regs..Something like 14.5 parts air, to 1 part fuel.. So adding K&N or other hi-flow air filter kit will make things worse....Then add hi-perf pipes it gets Leaner yet.. Gotta match the carb to the improved breathing..
Any carb coughing is most times a sign of a LEAN condition.. Providing ya don't have any intake leaks..
I don't care for the dyno-jet kits they add too much fuel & can wash oil off the cylinder walls & actually shorten the top-end life span..
You need someone to get at your idle-mix screw & adjust it say 2.5 turns out to start, & add a 45 slow jet..or one size larger than what is in there. This should get you in the ball park..