I had no requests at all and couldn't care less about specific trains until she sent me all the details and options... I only requested the Romance Car. She suggested the VSE 50000 and did in fact confirm it.

Anyhow based on all the feedback I've gotten, I think we'll try to leave earlier afterall. We'll still eat at Rokurishna but we'll catch an earlier train that will get us into Hakone no later than noon. I just wrote to my TA and requested an earlier Romance Car that could get us to Hakone by 12pm and we'll likely follow evergrn's very helpful suggestions for planning our day out.

Thanks again for all the feedback!