One thing I'd add, and this isn't gospel but my own experience, but I would barely call 270 an overshoot. For me, for almost anything that isn't a grill/sear etc., I aim for 250F. If it's anywhere in the range of 225-275 though, that's good enough for me and I find amongst all the other variables that we have to contend with, 20F each way is small change.
So while it's good to have a target, don't worry about stable temps to the nth degree. It can change due to wind, sunshine, even the position of your ambient probe moving a little.