Here's the almost-finished binding... almost finished because I've done things in an unusual order.
(Yes, brass eyelets. My client isn't willing to wait for a lottery win before she can order a pair of period-correct stays with handstitched lacing holes. Call it Rococopunk if you like. Which is different, incidentally, from Rococo Puffs.)
When you make a jacket, you mess with making pockets before you put the jacket together, right? Because it's easier to do the fiddly bits when you can do them on one smaller piece only, without having to wrestle the whole garment into submission.
So tip number one for binding stays is: bind 'em, then put 'em together, and then complete the binding over the joins.
Here's how I did the side seams after the boning and binding was already in place:
So now I have to bind over the joins, finish the straps (which will be totally detachable) and we're done!
Above, the outside in black wool; below, the inside in Chinese blue cotton.