Ok, an update...

SPG-generated miles posted a couple days after the AA-purchased ones, putting me over the mark. The Platinum status showed up today in my account. Therefore, the turnaround time was roughly one week. Maybe "the sweep" occurs on Sunday nights?

I had some last-minute business that popped up last week and I ended up hopping on five flights (three of which were AA), still while in Gold status. 2 of 3 were upgraded anyway Heading off with the wife this weekend, Platinum status in hand, as hoped for. Will report on the success rate later.

Thanks for all the help!