I think Cap1 likes there to be 6 months between CLIs. I'm not sure if an auto CLI is counted as one compared to one initiated by the card holder.... it might.
If you can PIF the whole thing, do it, not worth the bother of doing two payments. If you really want to CLI... do it after you make the payment and it clears.
What are your scores? Any baddies? Any other cards and what are those limits?
Hmm you have some good limits there, util is fairly low / reasonable.
I'd give the CLI button a solid try after you make the payments. I think asking for $500 more after an auto CLI should be an instant approval for you. Give them a call if you're declined. Not sure how much more you should try to ask for...
I was given a $500 CL with them initially and then given an auto $250 CLI after 4 or so months. I pay all my cards in full and 6mo or so after sticking with $750 CL on that card, I asked for $500 more online and was approved instantly to $1250. My card was paid off before I hit the CLI button.