Looking at the whole picture. Getting more credit doesnt help you gain much with baddies in the background. You need to take care of the CO's first. Then your scores will rise some more which would lead to better cards then than now. I know thats not want you wanted to hear. But you have to take care of the past so the future is better. More good than bad doesnt fix the problem. Or make your scores better.
Cap One has been great for me.
My first card starting rebuild and my first large limit card after rebuild started.
Are you prequal for Savor and Venture?
If so, I would get it if you want it.
It should be at least a $5k SL if prequal for Venture.
DON'T WORK FOR CREDIT CARDS ... MAKE CREDIT CARDS WORK FOR YOU!