Does resting heart rate change throughout a womans cycle when other variables are accounted for?

Sure, blood loss can lead to a lower hemoglobin, requiring slight heart rate increases. May be hormonal effects as well. I would expect the change to be small.

Rise in temperature in the second half of the cycle can raise the heart rate slightly, Cramps in the premenstrual period could raise the heart rate due to pain, blood loss during period may also raise the heart rate.