My Disney trip is from December 16-22nd and ideally I would be needing the 3x CLI for emergency trip expenses. I've been evalutaing this trip since February (11 months) now even way before I opened up this AMEX, so we do have a "saved up" budget. We got lucky on reservations and were able to bring down 7 reservations down to just 2 and feed the rest through Costco. On the 13th of December, my "next" commission check should arrive and there would be no problems in paying off the Platinum Delta in full. I'm just strategically thinking how to charge and pay off what in the right manner.
I would personally never recommend that anyone request a CLI if their utilization is above 28%. That's already at the worse end of the second best utilization tier. My personal opinion is that having reported utilization in the 1%-9% range is best. I think the second best would be on either side of that, meaning the 9%-28% range OR if you reported 0% utilization on the card. I think different lenders can look at these two utilizations different ways. Anything above 28% though, IMO, means you aren't giving yourself anywhere near the best possible look going into the CLI request.
I got a full 3x CLI on my AMEX BCE at 61 days with about 60% utilizaition (from a balance transfer).
OP, you'd definitely have a better chance with a lower balance but it's not going to automatically disqualify you.