Obviously I cannot prove it but I am confident much more Bitcoin moves OTC than on exchanges.
I''m not. If it were it would show up in blockchain analysis, at least under the category of "unknown". It doesn't. Most activity is fairly easy to categorize (speculation, mining, legal and illegal payments). Certainly there is some that isn't but not some massive hidden economy that is larger than all the known exchanges. It just isn't so
Where can one find such analysis?
How do you differentiate legal & illegal payments from OTC trading activities?
I don't know, maybe someone can point to some, but I've seen various reports published once or twice a year for the past few years.
The way you differentiate is by identifying what you can, and it seems a lot can be identified with reasonable confidence (probably not perfectly). If there is a huge swath of unknown that can't be then you ask these questions, but that has really never been the case.
Even gross statistics like coin movement on the blockchain relative to reported exchange volume shows a reasonably tight relationship over time. If there were massive amounts of money fleeing capital controls and FATCA now, that relationship would be break down (unless you think this was going on three years ago when FATCA wasn't in force at all and Bitcoin was $20). Instead it hasn't really broken down.
Don't buy all the hype. Some of it might turn out to be true, but be skeptical.