“Excellent” credit score with 1 maxed out card, will I be denied credit?

I have an Experian credit score of 736, which is considered to be “excellent” on www.freecreditreport.com
I have been very good about managing my credit card payments and I guess the score reflects it. However, I have 1 credit card with a $ 1,500 limit that has a balance of $ 1,450. I have been trying to pay it off but haven’t been able to for different unexpected reasons. I’ve just been making the minimum payments but the finance charges are almost as high as the payments themselves.
Anyway, since I can’t pay it off right now, I was hoping to get a high-limit credit card and transfer the balance, but I’m worried about being denied and “waste” a credit inquiry if I apply.
The reason why I’m planning on the balance transfer is because I know being maxed out looks bad on your credit score. So getting a credit card with a $ 10,000 or $ 5,000 limit, and transferring the $ 1,450 to it, will lower my limit-to-balance ratio significantly.
According to articles I’ve read, having a score of over 730 can get you the best APRs and you would think that getting approved for a credit card should be no problem, but I also know that lenders are very picky about having maxed out cards on your report.
Does anyone have any advice? Any articles that may clear up my questions?
I know the easiest way to find out is to apply for the card, but I really don’t want to waste a credit inquiry like that when I have the yahoo answers gurus to enlighten me before I do something stupid 🙂

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