Acquiring Russian The Natural Way

I spent a week in a country that has quite a few Russian speakers and managed to have a few short conversations with people from Ukraine, Russia, Poland, Latvia, Estonia and Azerbaijan. I also overheard several Russian conversations in public places. While the conversations weren't in depth it was great to converse with 'native' speakers. I was complemented on my accent and was taken seriously as a learner, not someone who has just learned to say привет and cпасибо. Just some more positive feedback and motivational fuel to keep me going.

It seems that the consensus is that native English speakers have the worst Russian accent. Have a look at some of the comments I found on a Reddit thread.  I wonder if this is to English speakers in general? I'd like to think I have a better ear than average for the nuances of languages but I may be wrong!  Anyway, this is one of the reasons I'm spending so much time listening to native speakers. It's not that I would feel self-conscious with a strong accent. I want to make myself understood as clearly as possible and make the experiences painless as I can for the listener. "English accent, though,  ugh. Especially the Judoon-grade chunkiness. Can. Someone? Figure! Out. Intonation? Already! Might be biased because that's the kind of Russian our crappy Hollywood representations tend to speak. The analogy I like to use is, English is like a pulsating spectrum analyzer (the thing with the bars for different frequencies); whereas Russian is like a rollercoaster — with ...