NB -- Good post. I'll make an exception from my perspective -- I no longer equate Sheraton with Luxury. I do recall when I would've many moons ago, but the Sheraton brand has morphed into what I'll call a solid mainline brand in logding, like Hilton or Wyndham (two brands which I find to be closest to Sheraton).
In general, I'd place the Marriott full service brand slightly higher than Sheratons (yes, there are exceptions, but I'm talking brandwide) and Westin a level above that. That said, they are all quite close in terms of brand significance.
Westin is an interesting brand with some challenges, too. Westin's growth pattern in the 1980s was to both build new, exciting properties in high profile locations and also acquire existing historic hotels in significant locations. Examples of the latter would be the former Westins: William Penn in PIT, Francis Marion in CHS. Today, the Westin St Francis in SFO is still with Westin and certainly falls into the historical category and outside the realm of modern luxury --- as defined by most of their target audience.