I know you are working on the baddies.
You already have the card history, you are just stuck with low limits. I'd try for CLIs if you can. If not, and you still want a card, then I'd try a secured card with a higher limit ($750 - $1000 +)
If you keep applying, assuming you get that card, you have several thing that may go against you: 1) more inquiries, 2) likelihood of more $300 limits, 3) decreasing history, and 4) when your scores improve down the road, you'll be in worse shape to app for better cards. I mention all of this from experience anyway. I'm stuck with $300-$600 limits. On top of that, because of the newness of my credit, even with quasi-OK scores, I have been likely turned down for 4 card out of my last 4 apps (Citi, JCPennys, CCCU, and Penfed).