Overpay (prepay) and having it available to use are two different things.
I think I'm in complete agreement, but allow me to just confirm what you're saying...
What do you mean by "available to use"? Let's say you have a $5k credit limit, a $0 current balance and then you prepay $5k. My understanding/speculation is that at Chase, you can do two $5k transactions in rapid succession and they'll both go through (no worse than doing a $5k transaction, paying off the balance mid-month, then doing another). In this case it is "available to use".
But you can't do a single $10k transaction. In this manner, it's not "available to use" as if it were a credit limit increase.
And my experience with Amex and Citi is that you would be able to do the single $10k transaction.