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The only time I asked for an increase was 90 days after I got it, and was declined because it said it couldn't offer more based on my income. But since it lets me charge twice my limit (up to 23k), its never been a problem.
I went ahead and app'd for a Platinum today and was approved with NPSL. Should I do the CLI request too? Does it make any difference doing that now vs another time?
I don't think the Paltinum card will have any bearing on the decision. As long as it's been 91 days since the denial the worst that can happen is they say no. Maybe they needed a reason before. Their limits are determined by a lot of factors and I think your heavy use of it puts you in a good spot. Best of luck and let us know what you decide and how it goes!