I don't have to worry about timing, such as shipping the day before check out? Or are they close enough for same day delivery (provided I drop bags for collection before a set time in the morning)?

It's about 110km between the Numazu and Yokohama hotels (~90 mins train, 2 hours road) and about 30-40 mins drive/train between the Yokohama hotel and HND.

When I did same day forwarding from HND to hotel in June, I had the bag dropped off at the HND counter by 6am and had the option of 7pm or 9pm delivery to Ikebukuro.