I'm not sure why I haven't explored simple Regency-style short stays as everyday bra wear before - they are surprisingly comfortable;
I joined the strap to the front of the bodice with a short piece of elastic (covered in the same fabric) to allow a slight give across the shoulders. I like a firm shoulder strap but do feel restricted in movement if there is no stretch at-all. From my research into this era I have found that they did use stretch panels that were made from metal coils, however these were not added to straps I don't think.
I would like to reproduce some more of the extant examples of stays and corsets from this era, including those with elastic panels. Here is an example from the Kyoto Costume Institute;
© The Kyoto Costume Institute
I can't find any photos of the front of the short version, annoyingly!