Thank you for reaching out to us.
We appreciate the sensitive nature of this question.
In this case, in particular because you follow Sefardi halachic rulings, it would be permissible to clean yourself out internally on day two or three of your period and attempt a hefsek taharah at that point, beginning your clean days earlier than you have been. If possible, in cycles in which you plan to do this, it would be preferable to refrain from relations in the few days before you expect your period. Based on your description, this step in itself may prove sufficient to enable you to immerse in time to conceive.
We also recommend that you see your physician to learn more about your current fertility, even though you are not interested at this point in taking medication to delay ovulation. There can be a number of reasons for a shorter cycle that may affect fertility in general. Anecdotally, some women report that taking alfalfa or even just eating breakfast every day can help extend the cycle. You could also discuss these measures with your physician.
To learn more about ovulation prior to immersion, please see our site’s article here. We also invite you to get back to us here with any further questions and to consider arranging a free consultation with a Yoetzet Halacha Fertility Counselor, details here.