Period getting strange over time?

Ka
To begin, I'll start by giving a little background. I have ALWAYS had really long, extremely heavy and very painful periods. Ever since starting this womanly horror I've had to double up on my products, I'd wear the largest size tampon as well as those large-enough-to-be-a-diaper but called pads to make you feel better, just to contain this insane flow. Yes, I've been to the doctor. Many times. Yes, I've had an ultrasound done and everything has come back in check. 
The females on my mother's side had a long history of these types of periods, as well as ovarian cysts and in one case, even endometriosis.
I haven't been found to have any of these issues yet other than the excessively heavy periods, which I was told was normal (for me).
They've always been regular, I even switched to a menstrual cup last year (best thing I ever did), but I've noticed with the last several periods they're becoming more and more irregular. They start later than usual, it started out just being late by a day or two but now it's around 4-5 days, and the last two of them, including this one, is having trouble starting. I feel the cramps, I'm spotting, but it just won't start.
I'm supposed to start a new birth control pill Sunday, I got my first pack Monday and that was the day I was due. I got this to control my excessive flow, but I'm worried now that something may be wrong and I should probably wait on these.
Is this normal, or has anyone else experienced this? Just the gradual slowing down of your period until it seems to be having trouble starting?
Is it something that should pass in time and is it still okay to take these pills?