You raise some really good issues, but I think petitions won't work.
They'll probably just say it's in the hands of different departments who take care of security screening, they have no control over how long they take for doing background checks, and so on and so forth.
One of my friends here in the US had a similar situation with a Visa, where they sent his file for additional background check. And when asked, they just say that it's out of their hands and it takes as long as it takes for the background checks as they are performed by the FBI and they have more important things to take care of than to expedite someone's background check for the purpose of letting them have immigration a month or two sooner.
This is of course just my two cents because I know of a lot of people who have tried with the immigration department, and failed.