I don't know the answer but I can tell you that I've been dealing with the same issue, though slightly different. I get menstrual type cramps around ovulation then nothing for about a week, then the week BEFORE my period I start getting mega-cramps (no bleeding). Once my period starts I have no cramps for a few days then BAM, cramps come on like no tomorrow. I always used to get cramps only during my period. I don't get the off-cycle cramping. I went in complaining about it last week and am having an ultrasound to check for cysts, fibroids and IUD placement. I have often worried that in the 11 or 12 years I've had this IUD in that it's either shifted or grown into my uterus. Probably an unfounded worry though.
Pretty much the only thing that helps my cramps is Advil (Ibuprofen). Tylenol doesn't touch them. Heating pads are great too.