The typical cards that people often open for balance transfers (Chase Slate, Bank of America BankAmericard, Citi Diamond Preferred, etc.) would be very unlikely to give you the starting line you're looking for when viewing the limits on your major lender bank cards. I'm not sure how you're getting 99% utilization, though. Running the math really quickly through that list of cards and balances, it looks like you're at under 50% overall.
I'd certainly look at all of your store cards that have 0% promotional purchases first before making payments elsewhere. Those usually have 6,12 or 24 month 0% APR offers, but if they're not paid off before expiration you pay interest (usually 25+%) retroactively to the date of purchase. So certainly pay those before you're hit with possibly hundreds of dollars in interest that you wouldn't have to pay by paying off those charges prior to expiration. After that, I'd concentrate on making sure no card was above 89% utilization (that's a red flag to lenders), then simply figure out which card has the highest interest rate and pay as much as possible until it's paid off, then continue to the next one. It'll still take at least a month before all of those new, lower balances get reported to the credit bureaus, but then you can evaluate your scores and decide if a balance transfer card may make sense for the remainder of the balances. Keep in mind that "what if" scenarios with credit scoring sites are just best guesses. It's also quite possible you may see only small gains by paying your cards down to under 30% - every credit profile is different.
