Well, when I was in House of Bruar last September I could have bought the whole store. :-) However, I think you are looking for a US source, and one that won't break the bank.

My favorite shirts for the money generally come from places you've mentioned such as LL Bean or Land's End, but you are right about the button down collars. If you look through their selections carefully you might find some things that will work for you.

Here's one from LL Bean without a button collar that is available in a small B/W check (not really a tattersall).

This one and this one from Land's End are more work shirts, but it lacks the button collar.

I also have to say that I have a couple of these shirts, and they are some of my favorites, despite the button collar.