Thank you again everyone!
I ended up ordering the Sailrite swing-away, 1" binding attachment. Definitely not the cheapest, but with the time and effort it will save me (not to mention what I hope will be a superior result!), it will be well worth it! I can't tell you how many hours I've spent and how many tears I've shed in abject frustration in trying to bind the inner seams of these instrument cases! (Though I do still expect to have a bit of trouble with the concave curves...)
Since I have to do these on every single thing I sell, I decided to go with the swing-away version for just $10 more than the stationary one.
Fingers crossed!!! And Macy- I'll let you know how this works for the cardboard-thick layers of a 3-dimensional case if you'd like! Maybe we can help save your husband some time and suffering!