Is the Shinkansen very crowded/busy in mid-April

Hi

I'm visiting Japan in early April and the last part of my itinerary is to travel from Kyoto to Narita airport the morning of my flight home. I'm wondering if I need to pre-book the train and NEX before I arrive in Japan or if I will be able to wait and book it once I activate my JR Pass (Green Car) on April 8th.

My itinerary for April 14th is;

9am or earlier(?) check out of hotel
15 min cab ride to train station
9:33am train (or earlier?) to Tokyo arriving 12:12pm - Hikari 644 Go train on platform 12
1:03pm train to Narita airport (NEX train terminal 1) arriving 1:57pm - NEX 27 Go platform Sobu Line underground Platform 4
OR
1:33pm train to Narita airport (NEX train terminal 1) arriving 2:31pm - NEX 29 Go platform Sobu Line underground Platform 4
1:57pm or 2:31pm arrive airport and check-in for flight
5pm flight home

Thank you for your help.