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IMHO, you have too many 'toy' cards anyway. Close ones that have annual fees first - 3-5 cards is what you ought to have. Work with those cards to get CLI's and grow them.
I think as long as you keep total UTI below 10% the total amount of credit won't make any signifigant difference - CLI's over the next 6-12 months while gardening should more than make up for the closed accounts. There *might* be a temporary score drop, but in the long run you will look better off, IMO. I don't see how closing the most recent accounts would hurt anything, if anything it will make AAoA longer. Just watch the UTI.