I just purchased my first Harley and have noticed it hesitates at low rpm and surges while cruising also at lower rpms usually around 2200-2900.
Also it diesels a little when I shut it off.
Also sounds like a good tune up is needed , I would try some sea wate for it , Lucas fuel treatment a small bottle is about $6 & a decent grade of gas run a tank threw & see how she does , heck cant hurt ,I use it & have for many years ,also at those rpm's you mentioned what gear are you in ?
i had something like that on my 85 fl. it turned out to be the 15 amp ignition circuit breaker was getting weak. i changed it and it cleared up immediately. you can get them at any auto parts store.
Pull the carb and give it a thorough cleaning. Spraying some carb cleaner in it will probably not clear the issue up. You're gonna need to get inside it and clean out the jets, etc. Check the diaphragms for wear. While you're in there, make a note of the size jets that are installed. On a older/used bike, there's no idea how many driveway mechanics, have been 'tinkering' with the carb.
The intake manifold seals may be getting dry and not sealing well. 'Could' be one of the reasons it's surging. Not a hard job to R&R, be prepared to cut down an Allen wrench to get at the bolts.
I'm not sure what carb is on it. I had thought about running some Lucas through it. I pulled the plugs the other day and they look good a little white like it's running lean. Usually happens in 1st gear when taking off or 2-3 when making a turn.
No mods that I can see, looks like original pipes but I can't see any baffles not sure if there were any from the factory. I will take the carb off and inspect it.