. . . this makes the twisties not so fun
I can believe that!
That you describe this condition as being confined to second gear makes the source of the problem
seem like the gear assembly in the transmission.
How long have you had the bike and how many miles have you ridden it with and without this symptom?
Have you tried starting off in fourth or fifth gear? If you have, does the engine stall or can you move off without too much trouble?
Have you checked the level of transmission fluid with an accurate gauge?
Have you adjusted the clutch according to standard methods or checked for appropriate free play at the clutch lever?