IF you've been to Japan before, no check in bags, and have mobile Suicas on iPhone, I think one could make the 5:20 N'ex to Shinagawa and the 6:37 Nozomi arriving in Kyoto 8:44pm. Assuming minor line at immigration, and if any line at N'ex ticket counter/machine just board using Suica and pay reserved seat fare on board. Purchase Shinkansen tickets via Smart-ex app and link ticket to Suica IC card number while on board N'ex - you will know which train you can make at Shinagawa (easy ticketless transfer). Take Green car if you want food and drink on train vs picking up at Shinagawa. https://www.jr-cp.co.jp.e.aau.hp.transer.com/services/
Anyway, I think you can make the 7:46 Nozomi.