Update: resolved. I received the check today, which is dated 3/3, the same day that I emailed the whole situation to the Diamond desk. Glad to see that the status means something, but it's pretty disappointing how horrid their customer service was up until I emailed diamond@hilton. I lost count of how many times I was told I'd be contacted "within 3-5 business days" just to never be contacted. Interestingly enough, the woman who responded to my email from the Diamond desk is the same one that responded to one of my prior emails to regular customer care.

All's well that ends well, I guess! Today I also received my card congratulating me on my lowly silver status. Time to enjoy my last stay as a Diamond in a couple weeks in New Orleans!