A near-complete rewrite. The button now matches Audible's own styling automatically, and the add-on is roughly 5x smaller and much lighter on CPU.

Improved

The "Play in Tab" button is now built from Audible's own button, so it matches the site's color, size, shape and font exactly. The stray border and the slight misalignment in 1.0 are gone, and the button will keep matching if Audible restyles the page.

Buttons now appear on library rows that load as you scroll, and after filtering or sorting your library.
Added support for Audible Germany, France, Italy, Spain, India, Japan and Brazil, including localised button labels.

Fixed

The button no longer occasionally triggers Audible's overlay player in addition to opening the new tab.

Performance and privacy

Removed the bundled jQuery library (89 KB) - the add-on is now about 5 KB.
Replaced a timer that re-scanned the page every 1.5 seconds for the entire time a tab was open. The add-on now only does work when the page actually changes.
Reduced permissions: 1.0 requested access to Audible product pages for a feature that never worked. 3.1 only requests access to your library pages.

Versions 2.x and 3.0 were development builds and were never released.