Competence and reliability and trustworthiness are in the eye of the beholder. You know how hard you work. You know how much you are stretched across many deliverables for many people. You know that you’re doing the best you can (and it is pretty damn good! (if you do say so yourself)). Others don’t know–or care. They know and care about what you do (and don’t do) for them. If you are regularly late for their meetings–or miss them altogether, then you are seen as disrespectful. They know that you don’t give them feedback when asked. They know whether you deliver what they are waiting for on time.
Whatever is in your head as an excuse (or a rationalization) about why you can’t make it to the lesser important meetings or deliver things for the priority 2 or 3 things on your list, IS IRRELEVANT to the people you are letting down. You appear incompetent to them. You are unreliable according to them. You better hope that these people never need to make a choice about hiring you or promoting you or downsizing you, because their opinion is the one that will count then, not yours.
It is way better for your future career not to overcommit, to be clear that their program, project, deliverable will not get done because you are assigned to other priorities, than to overcommit. We overcommit for a lot of reasons–to be liked, because we want to be involved in everything, because the person is a friend, or a former boss or an important person. Knowing your capacity and respecting your limits, even if it is uncomfortable, will keep you out of trouble. Learn to be clear about what you will do and what you won’t do. Learn to say no–or if you can’t/won’t–say no to someone else. No one gets rewards for all the things that they agree to do, only for what they actually get done.
The next time you are late or don’t deliver, see it through the eyes of the person you’re letting down.