Since you will be jet-lagged, it will be no problem to wake up early and catch an early Shinkansen to Kyoto, leaving most of the day to explore. Instead of stressing about catching the train to Kyoto that very night, I suggest taking it easy and having a relaxing evening in a hotel near Shinagawa.

On one trip, I had to be in Hiroshima by noon the day after arriving. I took the N'Ex to Shinagawa, where I had a hotel reservation. Since I was jet-lagged, I woke up at 4:30 and couldn't get back to sleep, so I had no trouble catching the 6:30AM westbound Shinkansen. That would have gotten me into Kyoto shortly after 9:00AM, if Kyoto had been my destination.