Doug,
I haven’t spent a whole lot of time tweaking my tail tune. I do believe that you need to set neutral position of the tail mechanically for hover that way if you are using I gain, it minimizes the amount of integrator that builds up and should reduce overshoots. @ChrisOlson posted on this topic here with a different method of setting Rate P and D gains that uses a low I gain. I think the big take away is that if you carry too much integrator in flight it will introduce overshoots in the response. Also that too much VFF gain will do the same thing. Hope this is helpful
Regards,
Bill