Based on your comments to anongoodnurse's answer, I've thought a bit more about this.
I still support the main point of anongoodnurse's answer - e.g. try not to hurt your daughter's access to her father if you believe seeing her father is good for her. But you're saying
My sanity is at stake at this point
If you really mean this - e.g. if you're near a burnout, then it is important that you reduce your workload and stress immediately. If you don't, you could suffer a breakdown that will hospitalize you for weeks, and full recovery might take months.
(There are several steps leading to a full-blown burnout, and each step has symptoms associated with them. You can google these symptoms, or better yet, get a professional opinion, to find out if you are in fact in danger of impending collapse).
Where I live, we can get partial sick-leave from work if a doctor diagnoses such problems. I don't know if that exists where you live, but if it does, maybe that would be an immediate short-term solution.
Once that's done, you might have some time to think your situation through and find a way to apply for additional help from the state.
I admit I've read over your question too quickly - I didn't read the following part:
to see her on his non-visitation days - which usually requires me to inconvenience myself in a minor or major way due to my work schedule
Is there any way you could change this without cutting off additional access to your daugher? Normally, I'd assume that having the father take care of your daughter would free up some time for you, not make it even more difficult for you. Is this because you need to be present when he sees her? If so, is there a way to change this so that him seeing her will actually free up time for you? If he calls and asks to see her tomorrow, maybe you could tell him to pick her up after school/kindergarden, and call the school or kindergarden to tell them her father will pick her up?
I don't feel comfortable suggesting this because you also say that he doesn't show up when he said he would, but the point would be that he's not picking your daughter up in your home, where you have to wait for him, but instead at the school, where a third-party (the school) will notice that he's not on time. That might put more pressure on him, and it will also allow for an independent record to be built that might be useful to have in the future. This way, if you do try to renegotiate child support payment and visitation, you have an independent third-party to support your claims that he's never on time. That might be especially useful if your ex is also late in picking your daugther up on his actual visitation days, which you might use to argue that he's not fulfilling his obligations as per the existing court order and that his inability to pick her up on time on his visitation days seriously hinders your fulfillment of other obligations (work, household work etc).
You'll also have to think about long-term changes. As I said, I don't think it's a good idea to try to force him to help you more using access to your daughter as a bargaining chip, for basically the reasons anongoodnurse mentioned. Really the only option I see is the one I already mentioned: Renegotiate child support payments and visitation rights. This might be in the form of a contract between you and your ex which can be enforced legally, or in the form of a new court order, depending on what works.
However, if none of the things I suggested works out, then you'll have to act to preserve your ability to care for your daughter. If you are hospitalized, you can't do that, and that will be worse for your daughter than being cut off from additional visits from her father.