Learn English – things have been pretty smooth until sometime

A. Working took place in the past. (A period of time is implied, of course, since you had to work for a period of time, but that fact isn't specified in this tense usage.)
B. Similar to A, but working took place over an unspecified period of time in the past.
C. Working took place over a period of time in the past. The tense specifies that there is a time also in the past that the period ended. (In your sentence, "until" is the wrong preposition; "before" is correct. Also, "before today" must imply "before your termination today"--which it does--to be correct.)
D. Working took place over an unspecified period of time in the past. My answer to C also applies here.
E. The person is still working here, and you want to know when he started. This isn't consistent with your scenario, so presumably that's why you don't feel comfortable with it. :)
F. It would be correct if the person isn't yet seeing his employment as being in the past. ("I have been working here for six years, and I'll be darned if I give up my job without a fight." would be an obviously correct usage, for example.) Once the person understands himself to be terminated, he had been working here for six years (when he was terminated).
G. Yes, I agree. "for the past six years" (or more often "for the last six years") should be used as "I have been working here for the past six years."

Your sentence as it stands has a number of other issues, so let's consider a simpler sentence:

The album orders haven't been sent out yet.

The album orders didn't get sent out yet.

In both sentences, the orders have not been sent at the time of speaking. If you wanted, as you suggest, to say that they hadn't been sent in the past but they have been now, you'd need to say:

The album orders hadn't been sent out yet.

As for "haven't been" versus "didn't get," they are more or less interchangeable. The only differences, to my ear, are that "didn't get" (1) is slightly more informal, and (2) places slightly more emphasis on the (implied) person responsible for shipping the albums out.