Purchased 05 SE V-Rod with 2500 miles last December and had similar problems accentuated when engine was cold. It too had sat around for over a year. I don't buy the light flywheel theory 100% but does make some sense and I was told by several that this is somewhat common complaint by owners of V-Rods. Had verbal fist fight with dealership where I purchased the bike over the problem until they changed injectors, drained fuel (didn't need it since I too had gone through a couple tanks), installed new plugs and allegedly remapped engine to run a little richer; mine was not only missing/stumbling but backfiring, indicative of lean fuel mixture. I had/have stock SE pipes, but heard that any exhaust system or air filter upgrade will cause havoc requiring retuning...you didn't mention either change.

Those changes by dealership and my allowing bike to adequately warm up after initial starting eliminated ~95% of the issue.

I agree too with the operating RPM issue. I was used to air-cooled HD's where I'd run comfortably at 2500-3000 RPM. But V-Rod seems "happy" at 3500+.

Good luck with this, Jack

 

Its just a thought, but I'll throw it at you. I may be way off. Sometime Throttle position sensor get worn or are just bad in certain spots. Can cause a pop or a back fire. Its on the throttle body. Should be 3 wire sensor. 1 ground 1 power ( maybe 5v reference) and 1 signal. You have to test the signal wire with engine off key on with a graphing multimeter. Twist the throttle with one smooth motion and watch the graph for any voltage drop out or when your riding it see if it happens in the same spot in the throttle, no matter what gear your in. Your bike has low mileage so I would not think it would be worn, but like I said just a thought.