Taylor has a whole new line of straps these days, and hopefully the leather ends are made thin enough to fit their ES end pin jack. The old suede Taylor-embossed straps (from 10+ years back) were perfect: the skinny end (that you adjust for length) was thin enough to fit onto the ES jack no problem. I have two of these and they are awesome. If you find one used I'd highly recommend it.
Fwiw, I'd personally never use any strap adaptor of any kind as it adds another potential failure point (or forget-to-do-it-right point) as opposed to a strap directly affixed to the endpin. Any strap can be easily made to fit onto the ES end pin (two coins, vise grips, and a few dabs of water is all you need). And if you don't have an ES, most any strap typically fits just fine; though, again, the end of your favorite strap is easy enough to mod such that it is a snug fit and a permanent no-fuss solution.
And yes, strap off the guit whenever in the case or (for me), guits on the wall hangers sans strap. Strap on the guit while on a stand is fine IF your are fastidious about keeping the strap out of a trip path. Yes, I've seen it happen to another player where the strap is partly laying on the floor with the guit on a stand (on a break) and someone's foot catches it while walking and blam ...down goes a guitar! Fortunately it was an electric and had a semi-soft landing so he dodged a bullet.
Edward