Are you still searching for clues?
Concerning your luggage, as long as your Shinjuku hotel can keep it (until you pick it up), you can send it in one or a few parcels by delivery service.
In order to collect your parcels by the night of the 19th at your Shinjuku hotel, itfs better to send them off before noon of the 18th from your Urayasu hotel (or a nearby shop of major convenience store chains such as 7-Eleven, Lawson and FamilyMart).
Also, items purchased in the Tokyo Disneyland (with some exceptions) may be shipped from the Home Delivery Service center inside the Park.
http://www.tokyodisneyresort.jp/en/service/detail/str_id:tdl_delivery/ In this way, I could rush to Fuji Safari Park and then come back for check in around 6pm at Keio Plaza. To speak frankly, that seems not realistic.
When you travel mainly by rail and bus, you need at least 3 hours (including time for waiting) each to get to then to get back from Fuji Safari Park; in order to explorer this park fully for its open hours in November (10:00 - 15:30), you should leave your Urayasu hotel before 06:30 and cannot reach your Shinjuku hotel before 19:30.
Or, do you dare to drive a car on the way where you donft know the routes well? (I cannot recommend that.)
[Timetables for shuttle buses]
Buses for Fuji Safari Park
: Gotemba Station (08:30) -- (09:04) Fuji Safari Park.
: Gotemba Interchange (08:50) --
Gotemba Station (09:00) -- (09:34) Fuji Safari Park.
: Gotemba Station (10:50) -- (11:24) Fuji Safari Park.
: Gotemba Station (12:40) -- (13:14) Fuji Safari Park.
: Gotemba Station (13:30) -- (14:04) Fuji Safari Park.
: Gotemba Station (14:55) -- (15:29) Fuji Safari Park.
Buses back from Fuji Safari Park
: Fuji Safari Park (10:53) -- Gotemba Station (11:28) -- (11:35) Gotemba Interchange.
: Fuji Safari Park (11:58) -- (12:33) Gotemba Station.
: Fuji Safari Park (13:48) -- (14:23) Gotemba Station.
: Fuji Safari Park (15:08) -- (15:43) Gotemba Station.
: Fuji Safari Park (16:43) -- Gotemba Station (17:18) -- (17:25) Gotemba Interchange.
: Fuji Safari Park (18:03) -- (18:38) Gotemba Station.
- Source in Japanese
http://www.fujisafari.co.jp/info/bus-time.html