With "accelerated greencard process" do you simply mean the greencard process as it exists for people that are already employed in the US as opposed to the slower / more uncertain process for people that, for example, use the Diversity Lottery or that are employer-sponsored but not already in the US?
I am not sure how it works actually. I know the Labor Certification part was skipped entirely and I was put in some higher priority queue. Whatever they did, it took just under 7 months from start to finish.