I have had this issue since brand new, and I'm not the only one:
2007 Rocket III Classic, stalling when coming to stop?
Stalling when starting warm
brand new R3 stalls out in traffic - YIKES!
Occasional stalling coming to stop
How did you fix your stalling problem?
And there's a whole host of other search results.
Having tried ISCV reset endless times, fueling adjustments, ignition timing adjustments, TB balancing, linkage cleaning/oiling, and then of course all the engine changes, it always amazed me this problem persisted... until 5 minutes ago.
How?
Stupid simple fix, turn the gold screw further in (won't be gold on yours).. This screw sets the minimum opening of the actual primary throttle blades directly. The ISCV isn't the fastest acting device and I believe the stalling has always been a result of it's lag between actually opening the blades far enough to prevent stalling, and being just a tad too slow to prevent it. By turning the screw in you're preventing the blades from closing so far that the bike can't idle, ISCV doesn't know the difference.