I don't know if this is your issue or not, but I'll share anyway. I have a 2007 1300S,(65K miles) same symptoms. At first I thought it was bad gas, drained the carb bowl, emptied the tank, put in fresh gas, no change.
I took the bike to a trusted bike shop near me house. After several hours of trial and error, checking everything from fuel, electrical, ECM, He decided to run the engine, and spray starter fluid through the exposed carb intake while attempting to rev up the engine. The engine did accelerate without issue. The tech took carburetor apart and found the plastic slide inside the carb had disintegrated. That was the good news, problem found.
Now the bad. With the bike 11 years out of production, along with Honda's infinite wisdom of creating this carb only for the 1300. So I'm out of service for at least 2 weeks. Only 1 dealership in the USA has this 100 dollar part. And if they won't part with it, Ordering from Japan is the only available option.
So good Luck, I hope you don't have the same issue/outcome as I'm living through right now.