You get hit for both total utilization and individual account utilization. So 27% total utilization is a little high - I believe you'll see score increases if you get that down below 20%, and again below 10% (I could be wrong on this one, but I think that's how it works). But just as important is how your utilization on individual accounts is. If you have any individual account above 50% utilization, that's a big hit, and anything above 30%, etc.
Others might have different opinions, but I'd first tackle any cards that are 'maxed out'. Get everything down below 50% (or 30% if you can), and then start getting down to 0% on a few of your cards. Don't use up all of your savings, because you never know what could happen, but use as much as you can which still leaves you a couple or few month's cushion. As long as you have a cushion, then anything over that should be paying down that debt (assuming the cost of servicing the debt is higher than the return on the savings).
