This just in from KDP Support:
I’m sorry for the inconvenience caused to you.
There was a temporary glitch in our systems wherein the payment mode that was selected as EFT was reverted back to the check mode of payment. Our technical team has been continually working on the issue and the same will be resolved shortly. You may go forward and update your bank account information once again on the KDP web site to receive payments via EFT.
Also, I assure you that your information has not been compromised and will not be available to any third party under any circumstances.
In the meanwhile, if you receive any payments via check, you may write back to us if you have difficulty in cashing the check and we’ll re-issue your payments via EFT as per your account information on the KDP web site.
I hope this is helpful. Thank you for your continued interest in Amazon KDP.
In a separate-but-equal email, I am told by Amazon Associates (!) that they have inadvertently mailed me a check for fees due, after first deducting a $15 check processing fee. The deducted money will, they promise, arrive in my usual bank account by EFT by the end of next week, and would I please just cash the check when it arrives. If for some reason I can’t cash the check, I’m to contact them again, and they’ll do an EFT deposit.
The internets. What did we do for fun before them?
. . .aaaaaand! Back to work.