Pay off all interest-bearing balances (that is, "old" charges).
Paying all accounts to zero will actually hurt your score, especially since your current level is relatively low.
You need to leave a small amount on one card - but if all of the charges are "old" ones, then pay them all off and re-charge one card for a small amount, to avoid having a zero balance but also avoid paying any interest. Then pay off that small charge once it reports, before interest accrues, and repeat.
It is beneficial to pay off all of your "old" debt to eliminate interest.
It is a temporary score hit to have all accounts reporting zero - that hit will go away once you have less than 10% reporting on one card.
The key is to make sure that less-than-10% amount gets paid off each month before it incurs interest, and then you re-charge something similarly small to keep the balance reporting on one card at less than 10%. Many people use Netflix memberships or something similar to that, a small monthly bill payment, to keep their small balance reporting, then pay it off immediately after the statement cuts to avoid interest.
