You would not have to wait the full 30 days to see the improvement if you don't want to. Part of what I do for my clients is help them with their credit and in situations like yours I can get your credit report updated and re-scored in about 3 days.
What I would do before hand is run a program that I have at my disposal through my credit reporting service called a "What if Simulator". In this case we would see how much of a possible improvement you would see to your scores by paying that account down.
Paying credit card balances down in usually the best way to improve your scores in the least amount of time. Of course, there are no guarantees but it is worth a try.
If you would like more details on your scenario please feel free to contact me at your convenience. Thank you.
Elliott R. Oliva