I got my response after a week.
I finally did, too, after seven or eight days from the time that I submitted the claims. Two were approved outright (one for under $100, one for under $200), but for the third, which was over $200, they requested the usual evidence.
Also, just to follow-up on what I wrote before about them putting claims into a "dormant" status if you don't submit the requested documentation within 60 days, I finally found the letter that they sent me a couple years ago when I let one of my claims lapse. The first paragraph reads as follows:
"Your claim has been placed in a closed status as we did not receive the required Proof of Loss documentation needed to proceed with your claim. We will not send you any additional correspondence on this claim. Please note that your claim has not been denied; however, in order to re-open your claim, we need you to provide Proof of Loss documents as described below. Upon our receipt and review of this information, we will be in a better position to make a determination regarding your claim."
Just FYI for anyone who hasn't experienced that before!