Recommended brands for full-day rides and short multi-day tours I’m going to be investing in a new touring bike soon for weekly centuries and the occasional few-day tour. I’m looking at the $2K or possibly $3K level.

I currently ride a Lemond Croix de Fer, and I like the comments I get from others who notice I’m riding a LeMond. So I find myself wanting to look beyond the common brands like Specialized and Trek. My question: is it reasonable to look beyond the common brands for a bike that is more "specialized" than Specialized?
Specific product recommendations are off topic here, but the answer to your general question is yes, it's fine to look beyond the biggest bicycle producers (Trek Specialized, Giant, Cannondale etc.)

Surly and Salsa are two brands that offer touring oriented frames that come to mind. (Note, I offer these as examples, not recommendations).