If bank receives investigation information from its core provider 1/27, is made aware of this information on 1/28, and per Reg. E must report the results to the consumer within three business days after completing its investigation (including, if applicable, notice that a provisional credit has been made final), but bank doesn't look at this information until 2/2. Is the investigation considered complete 2/2 and the three day timeframe starts the next day 2/3, 2/4, 2/5, so notice must be sent by 2/5?

As a consumer protection regulation, I would say that when the bank's agent completed the investigation, the bank completed the investigation. The fact that the bank opted not to read its email or failed to have a suitable procedure is not the consumers fault. It is more damaging when the consumer is harmed in this process. But because the bank chooses not to learn of the investigation is not a viable argument.