What do you mean by an "afternoon flight"?

Do you mean 1:00PM or 5:00PM?

If it's 1:00PM, you'd better follow hailstorm's route.

If it's 4:00PM, you have a lot more leeway. Make your way to Odawara somehow, hop aboard a Kodama Shinkansen, arrive in Tokyo, and transfer to the N'Ex. The trip should take approximately 2 hours, assuming that the next N'Ex is leaving fairly soon after you arrive at Tokyo Station.

You can book both your Shinkansen and your N'Ex at Odawara Station. All JR stations with booking offices are on the same computer system and can sell you tickets for any JR train or JR Highway Bus.