So I took it to my local PO today. This is the one I go to most of the time, where they kind of know me. I explained to the woman behind the counter what happened. And how it is my absentee ballot. Pour l'election americaine! After inspecting the oversized, over-texted envelope, she came to the conclusion that we had to cover up the two bar-code stickers, with my local address, on the back. I said, "But the front side is stamped. Surely they will see that?" She shrugged. She said they don't look for a stamp. That if they picked it up wrong-side first, they'd see the local address and fling it into the local pile.
I figured I had a 50-50 chance of it ever getting out of the country.
So I let her cover up the stickers. "That should do it," she said.
To the Belgian PO's credit, I did not have to pay again (though I had my receipt ready).
Royal Oak City Clerk's office will just have to cope.