Canceling a credit card or lowering your credit limit actually makes you LESS credit worthy. The MORE available credit you have the MORE credit worthy you are. Think of it this way, if I'm issuing you credit, I'd much rather you to have the ability to tap other credit lines if you run into dire straits, because it allows you to screw someone else, which is better than you only being able to screw me. Similarly, if someone else has given you a lot of credit, as a credit issuer I'd view that as a vote of confidence (unless you're carrying a large balance that utilizes a lot of your credit line), and vice-versa if you've been issued low credit limits, had credit lines reduced, or are maxed out on those credit lines. I would advise you to only cancel a credit card to avoid an annual fee at renewal or to reset the clock for a churn. It doesn't really make sense to cancel a card to free up credit lines before re-applying because it just makes you look less credit worthy. An issuer will lower your credit lines on the cards you already have, and if they don't you can ask them to do so when you call for reconsideration.
You didn't say what your score and inquiries were for transunion. If you don't have any inquiries on transunion then I'd try for the
35K US Airways Barclays card. Your scores are not spectacular to be honest, so I wouldn't go too crazy unless you see a really good offer. The 35K is a good offer for Barclays (45K if you count the 10K bonus if you pay the annual fee at renewal, for comparison to cards with a first year annual fee).