Taxi to Haneda Airport

Our flight back to Canada leaves at 10PM next Tuesday. We have 4 suitcases between 2 people and want to take a taxi to the airport from our hotel in Shibuya. We figured this would be easier than dealing with our luggage forwarding and navigating the metro before our flight.

I’m concerned about timing and when we should book our taxi. What time should we get to the airport? How early do we leave Shibuya? Is there rush hour during the evening towards the airport if we take a taxi? Is this the best option for us? We don’t mind paying the extra costs for a taxi as long as it gives us peace of mind and convenience.