First time with new guy, my period won't stop!

So I've been dating this guy for about a month and a half. We've been on 7 or 8 dates and are going out again tonight. I let him know early on that I wanted to take it slow but I've decided I'm ready now and really want to have sex. I'm an adult woman and am plenty experienced and comfortable with that decision. The problem is, I just restarted my birth control (Nuvaring - I had to miss a month) and in doing so it has extended my period indefinitely. It's hardly anything, just a small amount of dark fluid discharge. If I wait until the next cycle, it will be 4 more weeks and I really don't want to wait that long, but if I have sex with him now and there's a little brown fluid he might get all weirded out on me and it may ruin our first time. Down the road it wouldn't be as much of an issue, but so early on in a relationship it could really ruin the mystery. If I take the ring out now, I would have another full period and possibly longer, which seems like a worse idea. (I know, exceptionally bad timing on my part.) And I've heard of the "soft-cup" but have been told that a lot of times it can be unpleasant-feeling. So the question is, should I wait 4 more weeks or until my period stops? Or should I just go for it, turn down the lights, and hope for the best? How much of a problem would it be?