Hi

I did BA 7 in f last dec and immigration was very quiet ( out in about 40mins after landing)
I had lunch and breakfast but not sure of the current service ( what cabin are you in)
I had a leisurely lunch, then watched a movie, then tried to get some sleep ( it was getting dark outside by then due to winter)/rest then breakfast. I kept moving during the day after arrival ( walking around Yokohama with an afternoon shower at the hotel after check in opened) then out again in the evening and did not feel too bad the next day
have not used the luggage delivery service from hnd ( maybe ask in the japan forum) but think there are only a few places in tokyo for same day delivery ( in most cases it would be next day delivery)

Regards
Tbs