Hey thankful,
I have had a lot of help from my congresswoman's office. Of course you don't get to meet with the congressman, but they have their constituent representatives.
If you are trying to get the cis moving on a big scale for asylees, through your congressman, it is hard. But if you have a specific question or problem regarding your case, you will get an answer.
My experience has been that the congressman's office can get things done. Many people from my community have done it successfully. I have gotten one of my distant relatives a visitor visa through my congresswoman's office (if some needs specifics on that i will gladly explain).
But do give it a try, it is true that some offices are more helpful than others.
I usually just walk in (the constituent reps know me by now, but some offices require an appointment), meet with the rep, ask my question, they call their liason officers at cis, and i get an answer(or they send me a letter with an answer), and then it's time for small talk. For me, they have been much more helpful than the local cis io's.
It is totally worth a try.
Good luck and keep us posted.
AR