I recently also stacked my rings as you put it though purely by accident as my e-mail glitched and I didn't get my reminder mail till the week I was supposed to be ring free was over. I conveniently forgot this for a while three weeks later when I started my period the day before I was scheduled to take my ring out rather than the threeish days afterwards I was used to which caused me to momentarily panic. That period lasted till about when it usually does so I guess it was about four days longer than usual and I was cramping more but I attributed it to two months of build up. I brought it up that week at my yearly PPH check up and the doctor said basically what I’d assumed that this wasn't terribly out of the ordinary given the circumstances and as long as I didn't have further odd symptoms to not worry about it. That was about two weeks ago and no extra bleeding so far like you're describing. The extra bleeding does sound like the kind of "more problems" the doctors were warning me about though.
Not really sure this is at all helpful but thought it might be somewhat comforting to hear you're not the only one.