A few thoughts.
Basil, Most countries where a Visa is necessary have requirements to "prove" you will go home. Russia is no different. I can get an invitation from people I know for a 3 month Visitor status. BUT, I have to have a ticket home and they kinda want me to have a reason to come home like a job, house, family, money, stuff, etc. The J-1 "kids" that come here have to prove all that and jump through a few other hoops as well such as English proficiency. A few stay beyond their visa, and reside as illegals now. Personally, in my small area of the USA, the few Russians here "off the books" are better than the loads of Brazilians here "off the books". They don't segregate themselves, assimilate well and don't whore themselves. Meaning not here just for $, they genuinely like being here.

Hanna, Congratulations on Belarus! I have quite a few friends there but was basically told I couldn't visit by them. A fist-full of invitations by well respected citizens wouldn't do much good. "You are too American" was the consensus. That's too bad and too political and beyond my control or influence. My friends in the Trinity area have moved and I'm sorry because they would be good tour guides and hosts. They might even say I was a nice guy.
Yes, you screwed up. Russia is notorious for bureaucracy. This is a known factor for a visit. EU, Swede, Brit or USA. I visit Washington DC on occasion and have met some Russian Embassy staff "after hours". Most were very nice and offered advice about how to get a visa faster. A couple were miserable bureaucrats trying to live up to a stereotype. I wish you nothing but the best of luck. Perhaps a Master Russian will extend a Personal Invitation.

ALL countries set limits on immigration. Based upon many factors. That's reality. USA used to take in all Russians, not anymore. We are a big place, but we only have so much space. Mexico wants easier regulations to emigrate to the US. You should see the requirements they have for Americans emigrating!

Life is not fair. That's why it's called life.