Marriott does have rolling qualification that is checked, to my knowledge, at least weekly. It is technically unpublished and not provided on the Marriott website, but as you can find on Flyertalk, pretty standard and repeatable. I myself got Platinum once because of it.

As for when to get the credit card, I don't think it matters too much if you are going to be staying regularly. Just be aware the 15 nights will pop every year at that time. I would just get it right away because the 5x points you get per $ would out weigh this in my opinion. You would be giving up a lot of points depending on how long you wait.

Cheers.