It's definitely not true that you can't open new credit while you have a CCCS, at least not in my area or with the CCCS I went through. I have gotten 2 new CC's, an auto loan, and then refinanced the auto loan while doing the CCCS.
I did call 2 of the CC's that are going to close due to the CCCS and asked if I could keep them open. Both said no. The third one is already closed.
One of the ones that is going to close is BoA. That's the one with the highest CL. When I asked if I could keep it open, they said I could apply for a new one with them, but I'm guessing that probably isn't the best idea. The other that's going to close is U.S. Bank. The 2 that will remain open are Best Buy and Firestone.
I only have one late, on one of the bureaus, and it was over 24 months ago.
I'd really prefer a Visa. Besides BoA, are there any others that tend to be easier on CLs?