To make sure that our business is 100% legitimate, together with our planned incorporation in the US we will also register as an MSB and follow all guidelines by the respective authorities.
As for transactions happening within the blockchain and outside the exchange, it is pretty much understood that they cannot be tracked and we cannot do anything about it.
You should read up on Suspicious Activity Report requirements.
You probably need to know at minimum name, address, and DOB for every account holder. If people can generate anonymous accounts and transfer thousands of dollars between them, your AML plan portion of your MSB application probably isn't going to be approved.
I am rooting for you, but I don't see how you will be able to get a MSB license in the US.