Online MTM is the way to go.
Mytailor/Hemrajani has Acorn fabrics in the $200 - $250 price range.
Proper cloth has the best website and are NYC based so you can be measured in person. Their fabric selection is limited, but well curated with classic patterns and colors. They have Thomas Mason, around $150.
It seems that one of the best strategies is to invest one great fitting bespoke shirt (or 3 or whatever the minimum is), and then send that shirt to one of the online...