It seems like the two biggest pieces of feedback have been:
i) identifying exactly the right market
ii) distinguishing from the competition
My current job is actually in strategic planning for one of the major ad agencies, so I've got some experience with both these things. Obviously I wouldn't be trying to go to market without having done significant thinking on both these issues. One of the reasons I started this thread was to get a conversation going to help me think through these sorts of things. In other words, I don't have the answers yet, so I thank you guys for pushing me and helping me toward finding them.
My current thoughts on target audience are men, 25-45, working professional jobs that require them to wear suit/jackets/shirts/ties on a regular basis, if not daily. He enjoys wearing the uniform, but has just enough of a dandy streak to want distinguish himself in some small way. He appreciates classics, but doesn't want feel like an old guy. Does this represent some gaping hole in the existing market? No. But I think that's okay. Distinguishing oneself too much from an existing market leaves one with a very small target.
I think the bigger way to distinguish from the competition is through user-experience. One of the major trends in men's clothing retail over the past few years has been an increase in customer-service/user-experience aspects. Fields may be a great tailor, but it is inaccessibly expensive for most people. On the other hand, walking into a mass retailer looking to buy a suit is a pretty horrible experience. I think that Cuttingboard's mention of The Armoury is a helpful comparison. One of the things they've done really well is make a very good user-experience.
The other thing The Armoury has done very well is what LAGuy talks about as 2013 Marketing Strategies. A strong social media presence allows you to build a reputation well outside your immediate customer base. The idea of having shallow, constantly rotating inventory gives you material to constantly be posting on social media, engaging with the community, and getting people in the store more often. Fox&Co. may have a great selection of classic menswear, but they are selling/marketing in an outdated way. The niche may be in applying contemporary marketing and retail techniques to selling classic menswear. This is what the Armoury has done well, that very few other brick & mortar stores have.