Hmm. I can't really respond in Russian, nor am I good at explaining, but I will try.
"We have got a very good boss." is broken English. You do NOT need the word "got" for that. I think you are thinking of "We have gotten a very good boss.", which is a bit of a different sentence than the one we have here.
I give you a scenario. A group of people know this person who is a very good person at doing things like managing. Let's call him Вадим. Вадим is then nomimated(chosen) as the boss. After the nomination, the group of people say, "We have gotten a very good boss! Yay!"
Another scenario this time, related to that same boss this time. Imagine an interview. The interviewer asks a worker of the company, "How is your boss? Is he a good person?" Since the boss has ALREADY been chosen in the company, the worker replies, "Yes, we have a good boss."
CONCLUSION(?): So there is this "уже" that is already implied in the correct sentence. While the one with "gotten" is like a "at that moment" thing. I hope this helps.