UT is utilization i.e. percent of your available credit that you are using.
Your best course of action is to contact the lender(s) where the late payments occurred and ask them if they would do a goodwill adjustment to remove the late payments reporting to the credit bureaus. If you search for the term "goodwill letter" you should find lots of examples of effective letters. This thread should be particularly helpful to you: The Saturation Technique: Best GW adjustment odds.
As previously stated you don't need additional credit cards. If you pay down your current balances so that your aggregate utilization is below 28.9% you should see a bump in your scores. You will get an even larger bump if you can pay your aggregate utilization down to below 8.9%.