I would definitely wait on closing any cards. And depending on what companies you are doing business with, it is possible no matter how low your balances that you might be eligible for an increase or in a position to mature them a little more and get an increase.
For instance, if any of your cards are Bank of America, increases are now all soft pulls so you will no be adding any inquiries if you ask for a higher limit. I wouldn’t ask for more that doubling it and you would know if you had a chance by logging on to your homepage to see if the increase link is there. If they do deny you, wait 3 months 1 day and repeat. This will not hurt you as these will continue to be softballs.
Some people have a number of cards issued by Comenity - store cards usually. These have historically been soft pulls to get a CLI. If you have any of those in your portfolio it might be worth a look but I definitely agree you want to be over a year in age before you give it a go.
Also, don’t be in a hurry for your loan to report at zero. You will temporarily see a drop in your scores - that’s the way Fico always deals with paid loans but you’ll bounce right back to normal with time.