So I heard back from the embassy today.

Granted, it was just a letter going "send us money, and not a check!" But still, at least it means they have officially gotten/seen my application.
Bit of a fail on their part with reading comprehension, though, since I said in my cover letter that the reason I wasn't including CC info with the mailing was to avoid sending my CC info through the mail, and today's letter requested that I mail them CC info.

They also provided a phone number to call with questions, though, so I just left them a voicemail message with the info. (I don't know why, mentally, that seems more security-conscious to me, but it does!)
So yay, forward progress.

And my pets have an appointment on June 22 to get their blood drawn for the rabies titer.