Hi Miranda!
I know that I can't totally clear up the math route for you...but I will tell you what I do know.
Discovering Mathematics 1A picks up where Singapore 6B leaves off. I don't think there is any reason to do anything in between 6B and DM 1A unless your student was really struggling with something and needs it. I think that Math Essentials has been mentioned as an optional program to help get a child who has some weak spots in their math learning "patch" those up before heading into high school stuff for math & science?
I know that the DM series will include some algrera and geometry mixed together throughout the books, so there's not just an "algebra" book....but you will cover it all throughout them.
I'm guessing that if you're not going with DM, you'll want to choose one of the other algebra options to begin after 6B.
How did the doubling up go? I know that I was wondering if I needed to do that with my oldest (who switched to Singapore in 3rd grade, but needed to do Singapore 2A). I had a chance to see the rest of Singapore's books and the DM series and talk with Julie, and there was no need to speed along. Grant will have the opportunity to do all the advanced math he'd like through high school, including algebra, geometry, trig, pre-calc, if we just stay moving along at the pace of a workbook per semester. So, he'll be using 6A & 6B for 7th grade this coming year. If he didn't get it all, you can feel free to back up a little and make sure it makes sense. That will probably be more important in the long run than having the level of the Singapore book match grade level.

Kathleen