Gotemba to Shinjuku with Hakone Free Pass

i plan to buy the Hakone Free Pass with the roundtrip travel from Shinjuku.
But i plan my itinerary so that my last stop is the Gotemba station and Outlet Store.

I can't seem to find which train or bus to use to get from Gotemba to Shinjuku which i can use the Hakone Free Pass.
As much as possible i don't wanna go back to Odawara from Gotemba just to catch the Odakyu train that can take the Hakone free Pass.
Hyperdia is showing me to hop on a JR train to Shin-Matsuda then get on the Odakyu Odawara express train to Shinjuku. Will this Odakyu Train in honor my Hakone Free Pass if i get on it at Shin Matsuda Station?
or do i have to get another separate ticket?

or is there a better faster alternative going back to shinjuku with the Hakone Free Pass?

As much as possible i don't wanna go back to Odawara from Gotemba just to catch the Odakyu train that can take the Hakone free Pass.
That is the point of the Hakaone Free Pass - it uses Odawara as the gateway to the region. If you don't want to go back via Odawara, select a different (non-HFP) option. You may not have noticed the location of Gotemba on a map and the transport links and who operates them.
The map on the Odakyu page for the Fuji/Hakone pass covers a different route back to Shinjuku for you, but if you want to go direct (bus) or train, it won't be via Odakyu.
https://www.odakyu.jp/english/passes/fujihakone/

Just pay to get from Shinjuku to Odawara, buy the cheaper free pass for 4000 yen at Odawara, then pay to go from Gotemba to Shinjuku.