I don't think that you have to give up your Russian citizenship when you become a permanent resident of the USA (or even become a lawful citizen of the USA). I'm pretty sure that you can have dual citizenship in Russia as well as in America.
My problem is that I came to America when I was 18 years old. Now I'm almost 21. According Russian Constitution you have to exchange your passport when you turn 20. So my Russian passport has been expired for almost a year. Legally, you have to show your presence to exchange your passport, nobody else is eligible to do it for you, but you know how it is in Russia- you can pretty much talk to the right people and get whatever you need. So my Mom is going to do it for me. I just have to get a power- of- attorney from the Russian Embassy.
I think you shouldn't worry about it. If your "zagranichnyj passport" is not expiring anytime soon I'm pretty sure you can use it as identifying document of your Russian citizenship IF somebody will decide to question you. And you'll just renew you Russian passport whenever you get there.