I didn't have the contractions so close together, and I only had BH contractions up until I delivered, but I was about where you are, being 50% effaced and 1 cm for about two weeks before I was induced. I was induced at 40 1/2 weeks. My doctor didn't want my baby to be too big to deliver, so she pushed inducing with me. It all worked out the way it should. But, I hope for you that you get to go when it's really time. Maybe those contractions will help speed things along for you. :-)
I was 50% ant 1cm dilated for a month before my cervix changed to 2cm, and I was having regular BH contractions. The day I turned 38 weeks I went to L&D because my pelvis and back were killing me and I was 80% effaced and 3cm dilated. I had my dd the next morning after having gone into natural labor after I was told by a nurse I wasn't in labor. lol. It's hard to say, you can be 1cm for a month, or you can go quickly. I went from 2 to 3 in a week or two.