On the inbound, HND to Kanda, your arrival should be early enough to avoid the evening rush.

On the outbound to NRT, you can minimize the time in the packed commuter trains by alighting at JR Ueno station and catch the Skyliner train train at Keisei Ueno station.

Another option is the LCC bus. It is about 1 km from Kanda station to the Yaesu bus stop, may be closer or farther depending where you are staying.

Yamanote line and Keihin-Tohoku line run parallel to each other on the same platform from Shinagawa to Tabata. You can hop on whichever comes first. However, Keihin-Tohoku Rapid trains do not stop at Nippori among other stations so don't get on it when you are going to NRT via Nippori.