Now the problem is how to be able to invest when the coin is cheap.
Planning how practically to execute the sale of the bitcoins is also important. You cannot suddenly repatriate millions of dollars to your bank for example (the limit of "suspicious activity" may be much smaller such as $5k!).
I am not sure what you are talking about. Surely, exchanging money between bank and brokerage or between bank and coinbase is NOT a "suspicious" activity.
I think that coinbase undergoes full KYC/AML vetting procedure (takes a month).