Imma be that guy, sorry.

So many of my favorite films of the western genre are in fact deconstructions of it. A lot of them involve the aging cowboy, facing obsolescence in a world that is changing from the wild west into something more civilized

That isn't a deconstruction, that's the main western myth of old west vs new west. It's basically the hero's journey, ground zero, of the western. Western isn't just "any movie set in the American frontier."

The Good, The Bad, and The Ugly doesn't fit that trope though, neither does The Searchers, Butch Cassidy, or Unforgiven (which is a deconstruction but isn't Old vs New West).

Shane, Proposition, Open Range, and Pale Rider do fit the trope.

Anyway, to answer your question of what are good Westerns that don't do the usual Western mythos:

Johnny Guitar

Rio Bravo

Stagecoach

Appaloosa

3:10 to Yuma

High Noon (which is an actual deconstruction)