The Shin-Osaka->Hakone->Tokyo itinerary is quite feasible; I have done it myself few years back. There are Hikari trains that stop at Hakone every two hours. Try to leave no later than noon and you'll be in Odawara before 3 PM. Depending on where the hotel is, it can take up to an hour to get to Gora, for example.

While the Odakyu Romance Car is the simplest way to go from Shinjuku to Hakone-Yumoto, it still takes 1:40 and you can't use JR Pass.