You don’t need a full-time COO to succeed.
A COO's main job is to help others succeed, not to become a shadow leader. Limited time forces the creation of self-sustaining operations. It is best bang for your buck.
Also, change happens gradually, and full-time doesn’t always mean more impact. Especially if the role is paired with a junior full-time operator.
Unless the COO is assuming the leadership of the entire organisation, a part-time role is likely the best fit and worth considering.