Ya on arrival, spend the week in tokyo.
On day before checkout, let the hotel know u want to use luggage service to send your big luggages to the Tokyo Bay hotel.
The hotel should know about the luggage forwarding service, common in Japan.
On day of checkout, leave your big luggages with hotel n pay the fee for sending to Tokyo bay hotel.
There is more info on luggage forwarding on this thread
https://forums.hardwarezone.com.sg/threads/all-about-luggage-forwarding-in-japan.6876209/
After Hakone, just go straight to the Tokyo bay hotel n check in.
Let them know about the big luggages n collect your big luggages at the hotel.
Hakone n Mt Fuji, u can drive if u want but i think public transport is easier n u dont have to worry about parking, car n return car.
Ya suggested Narita town for last day as your flight to sg leaves at 8am which is quite early.
If stay near the airport, dont have to wake up so early n less chance of interruption when getting to airport.
Less stress too.