If you have the limits to support it, balance transfer the total amount of debt to one card with a 0% BT promo(normally there is a 3-5% fee, but this would be worth it in your case). I know Citi and Barclays only reports 1% of the statement balance as the minimum payment on your credit reports. I have never attempted a BT on any of my other cards, but if you have a $6000 balance your minimum payment would only be $60 with Citi or Barclays. The kicker, make sure you pay it off BEFORE the promotional rate expires!
So you could have a really high CC usage, but if you happen to have really low payments on your credit report, that's all they care about? The monthly payments?
And not the total debt?
It may also be worth noting that spreading it out on multiple cards will lower your FICO score. Number of CC accounts carrying a balance is a factor.
Exactly what Pakman said - it'll be much more beneficial to keep it on one card, and NOT spread out.
In my situation, both my Citi TYP and Barclays Apple Visa have 20k limits, so a 5k BT won't hurt utilization too bad(total CC limits are around 110k). Boober - even if you had a 10k limit card(in addition to others), I would do this to help out your DTI for the house.
I keep my high balance on one card and keep the others at zero come report time. I think it's easier and looks nicer on paper to have just the one payment rather than a bunch of payments across multiple cards with different minimums. But I have noticed with my NFCU cashRewards card if you make another payment after the due date and before the statement cuts, the minimum monthly payment will be $0 (even with a balance).
In that case, I don't know how they calculate it.