Craig,
When you say Weber, are you on a charcoal grill? If so, I go cook using a two zone method, coals on one side, and the chicken is on the other side until it gets close to target temp. When I cook the chicken, the chicken side of the grate temp is around 325-350. Once I get to 170* or so in the thigh, I’ll move the chicken to above the coals and finish to target temp/crispy skin.
But yes, you want hot coals to finish, even if you are going from SI to Weber. If a Weber gasser, I use high on all four burners on my gasser and finish that way.
Hopefully that helps?