For people struggling with the past participle:
You normally say I haven't done X yet.
similarly if this statement happen in the past then it would be I hadn't done X yet. So ans A is fine, because he had yet to change his registration at that point in time, in the past.
B is unclear:
B is ok in my view but A is better
on interpretation could be there were numerous registrations he was trying to change, and he had done others but not for the "registration at the moment of his nomination" yet
C: run on sentence without puntuation
D: to be honest I don't see a problem with this sentence. Some explained above that was changed lacks the timing element, that is not a problem either.
It is the same as trying to differentiate:
i) the work is done
ii) the work has been done
they are the same but the messages are subtly different, the emphasis of (i) is the fact of the status of the work being done, while (ii) emphases the achievement of work with some focus on timing, ie the focus is the task was done some times ago rather than focusing on the achievement of the work "it is done!"
the only thing I can pick on this answer is the passive voice - "was yet to be changed", ans A is marginally better
I'm afraid I don't buy the OG explanation of modifier placement and ninja's explanation of time sequence
E: again, this is a totally understandable sentence to me, but gerund is generally not accepted in GMAT as it can be confusing (verb, noun, modifier?)