We will definitely have to save. Its just hard because to get it done publicly you need to have a fair idea of when cd5-10 is because thats when you need to have it done. But by the time I will find out when that is (because of such irregular cycles) the appointments are filled. At least by going private you can guarantee getting in whenever you want at little notice.
Could you make several appointments so that you have one a week for a month or so? So when the time comes, you should have one on the right cycle day and you can just cancel the others.