For what it worth, when I applied for my first credit card in college, I was the authorized user on my parents' 8-year-old AmEx with a $30K+ limit, and I've heard that creditors like to see AmEx on a report. It still shows up on my CR now and I probably owe a lot of success to that.

Do you have any way of getting added as an authorized user by a relative or close friend? You don't even need to spend on it, just have it on your report.

Btw, 7% utilization on your Cap1 is only about $55, which is less than the annual fee for these cards. Prove to Cap1 that you spend on their card and pay your balance in full, and they should be better about upping that limit. That may mean having a high utilization one month (your score will have a temporary dip), but if you pay it off in full, it'll help prove that you can handle the credit (which is what creditors want to see)