There are different differences within the examples as presented (which I'm sure aren't exhaustive regarding possible distinctions, but let's stay focused).
1a: We've been accustomed to working together.
1b: We've got used to working together.
1c: We are accustomed to working together.
I've included a third alternative because that's a more common version that most closely matches 1a in implication (working together is what we're used to / expect). 1b could imply we might not even have wanted to work together when we started (but now we've come to tolerate, bear, put up with the situation.
2a: It takes you a long time to get used to it.
2b: It takes you a long time to be accustomed to it.
2c: It takes you a long time to become accustomed to it.
Where 2c replaces non-idiomatic 2b. I can't really see any scope for saying either version could imply anything different to the other. I'm sure 2a would be far more common in relaxed speech, but there's wrong with the slightly more formal 2c.
3a: He got used to finding fault with everything.
3b: He is accustomed to finding fault with everything.
Where 3a implies that he didn't want to keep finding fault(s), but they were there and he couldn't avoid them (perhaps he worked as a Quality Inspector). After a some time, it no longer bothered him that he had to keep finding fault(s).
3b, on the other hand strongly implies that he does want to find fault. Similar to 1a above, in that the implication is he both wants and expects to do so.
4a: I've got used to drinking my liquor neat.
4b: I'm accustomed to drinking my liquor neat.
Unquestionably here, 4a implies that originally you didn't like drinking neat liquor, but you had to do it so often you can now at least tolerate (and even perhaps enjoy) it. Whereas 4b might be a somewhat "imperious" request / command (Give me a glass of neat liquor, because that's what you normally have, and it's what you're expecting now). Or a withering complaint, if you've just been handed a glass of watered-down whisky when you wanted it full strength.
The main difference (apart from the fact that used to is much more common than accustomed to), is that usually, to be / get used to is more closely associated with adapting to a situation (through past exposure), whereas to be accustomed to often implies expecting / wanting some past pattern to be repeated in a current or future situation.