45-day letter: The FAQs were pretty clear that this letter may not leave the FI until the 46th day, nor could you force place until the 46th day.
By way of example: If the 45th day were a Friday, the letter nor insurance could be mailed/put into place until 12:01 am on Saturday. Using your April 1st example, If the 45th day were 4/1 then the letter could not be mailed until 12:01 am on 4/2.
FEMA lapses: If you have FEMA policies for your customers and the Government shuts down, your policies are no longer valid. There is a 30-day grace period worked into all policies. So, if the Government is out for longer than 30 days you would have to start force placement activities starting on the 31st day. Your 45th day start time starts the day the Government shut down or failed to reinstate insurance. Yes, private insurance policies would be the route to go if this happens.