Presumably their role is not to sit in meetings all week and there are actual expectations of delivery. If you just shrug your shoulders and tell your manager nothing got done again because too many people booked meetings with you - don't expect to last long there. Your time management is on you. Working overtime is one way of dealing with this, a bandaid, but a common one. What op is trying is a way better approach and I think deserves props. Others' demands on your time only get worse the more senior you are.