It seems that your highway bus tickets should be purchased by the time 10 min. before the departure, i.e. 8:00 pm.
Even when you take Shinagawa route, presumably no escalator or elevator is found between Track 15 and Central West Ticket Gate.
If the day falls on a weekday, you may encounter an evening rush.
And, there may be passengers in a row at the ticket counter, including those who hope to manage to reserve seats.
Maybe it's better if one of you goes to purchase your tickets (with no baggage items but a wallet) and the others carry your baggage. The purchaser is the one who has reserved your tickets, or if not yet, anyone who has reached 20 in age.
From JR Track 6, probably you can go down via an escalator to the concourse and turn left at the first corner towards Central West Ticket Gate.
From JR Track 15, you can go to Central West Ticket Gate via one of two stairs in the middle of the platform.
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i found this website, which is a great help. Keio: Guide map (in Japanese) of Shinjuku Stations of several operators
http://www.keio.co.jp/train/station/station_map/pdf/ksb...On this map from the bottom, there are 16 JR tracks, 10 Odakyu tracks, and Keio station.
The writer of the article is saying he/she advanced under JR tracks, went down via a stair near Central West Ticket Gate, advanced under Odakyu tracks, went up and got out though a gate in Keio station building, and advanced towards the bus terminal.
Good luck!
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