An American can run around Moscow all he wants, and the more fluent he/she is, the more the authorities will take a dim view of his/her activities. If he/she's willing to pay major money (nowadays much more, due to inflatsiya) they could always find many willing takers. Of course, they'd probably just end up with garbage.
Years ago I thought I was going to write a book on "Lost in Space" cosmonauts, and found lots of people who wanted to give interviews about things that never happened. They even could produce photos and documents. One scientist was an equal-opportunity "deep throat" - he had suitcases full of data on NLO (UFOs), remote viewing, psychokinesis, and whatever you were interested in. But alas, all fake.
Where an intrepid investigator might have better luck might be in the archives of a former non-Soviet Warsaw Pact member state, or former Soviet republic. Some good data may have been overlooked in the basements and attics of say, the Bulgarian or Ukrainian security services. You'd have to make sure that you weren't being set up, again, with data to make the Soviets look bad (I mean, worse).
Viktor Suvorov recounts some humorous anecdotes regarding "state secrets" overseas in his book, Aquarium.
I am thinking something in Germany (former East) or Czech Republic might yield something on VVAW 1971. Too bad the window of opportunity closed compared to the earlier days.