mathanxiety I find it odd that nothing in any of what you posted gives you a hint of the meaning.
Exactly. In any other language other than, it seems, American English (from what has been so forcedly pointed out by some on this thread), you have strict rules regarding tense:
I have got
I did get
or
I have
I have (archaic) either gotten/begot
With "gotten", it seems to substitute for proper use of tense and you have very little idea what it means. The current American use of gotten appears to be incorrect.
I also find it sad that there are people out there who have such little knowledge that they think the use of English was fixed by Shakespeare or Milton and that fixed RP some time around their times, without taking account of any regional variations that weren't fixed then at all. But as a result of that lack of fixing presumably, "gotten" fell out of use in the English language, and I find all these attempts to say that it is not a bit fake. Its more of a fashion trend at the moment, rather than resurrection of some fixed archaic use of English.
What is wonderful about English is that you can still hear the echos and the patterns of speech of other Germanic languages from the same family from which it is part. If you have any knowledge at all of these languages, you realise the importance of not over-emphasising Anglo-American cultures at their expense. Not lest because some of them were still spoken in parts of Britain until relatively recent times (in a historical sense).