Often when people are paying off credit cards, the two most common strategies are
1) Highest interest first. This saves the most money
2) Lowest balance first. This allows you to feel the progress of paying off a card fairly quickly. (If your highest interest balance is large, then strategy 1 sometimes feels like little progress is being made, as the balance decreases slowly)
In your situation, 1 and 2 are the same, so the choice is clear!
You mentioned CLI possibilities and this really shouldn't be in the picture. Paying off Barclays rather than Target means you are losing real money against a somewhat nebulous chance that it may make it more likely to get a CLI. With Barclays, no way of knowing at all! Worry about that when interest charges (and utilization) are lower, and the best way to speed that up is, like everyone says, paying Target.
