I never had any problems buying a Nozomi Ticket upon arrival.

Transferring at Shinagawa is convenient as the N'Ex and Shinkansen tracks are very close and use the same concourse. But the two Shinagawa bound N'Ex are at 17:44 and 18:48.
http://jreast-shinkansen-reservation..._nex_u/04.html

17:44 train will be too tight for 17:00 arrival. 18:48 N'Ex will arrive Shinagawa at 20:02 and give them plenty of time to catch the 20:17 Nozomi. There will be two more trains 10 minutes apart each and a third train 20 minutes after that.

Below are from Hyperdia.com

Route Departure time/Platform Arrival time/Platform Total sum
The first SHINAGAWA(20:17) KYOTO(22:28) 13 ¥13520
The second SHINAGAWA(20:27) KYOTO(22:41) 13 ¥13520
The third SHINAGAWA(20:37) KYOTO(22:50) 13 ¥13520
The fourth SHINAGAWA(20:57) KYOTO(23:08) 14 ¥13520
The fifth SHINAGAWA(21:07) KYOTO(23:18) 13 ¥13520