Formerly, Aeromedical had a policy of placing priority on those who earn a living with thir medical; that policy has been disregarded the past few years. There is some belief that becoming a regular caller makes on an "interested party," and some are of the superstition that it increases one's velocity through the SI process. I'm reluctant to believe in bigfoot, flying saucers, or a leg-up at Aeromedical, but like the magic rabbit foot, it can't hurt.
Keep up with phone calls to your regional flight surgeon, and to the national line, calling on non-consecutive days.
Introducing a congressman to the process isn't actually going to speed it up, and may very well slow it down for the person doing the calling, and for everyone else, too.
If one doesn't want to spend the money for AMAS, sign up for AOPA and use their professional services program.