I forgot to update this post after I flew IAD-NRT-MNL and then MNL-NRT-LAX a few months later. Overall, flying with a pet in cargo on ANA was really easy.

I made sure to buy a crate that was within ANA cargo requirements. I had all the paperwork for the destination countries (Philippines & USA in this case, which was just rabies immunizations). I can't remember any special paperwork I needed for ANA, though I do remember needing to mark the crate and have ID so ANA could make sure I was connected to the crate. Then I gave my dog to the ANA checkin staff at each departure (IAD/MNL) and then had to get the dog from the special cargo window at destination. At NRT, I was met at the jet bridge by an ANA rep who confirmed that I had a dog in transit, and I think one checked when I left NRT. Past that, nothing special. It was really easy overall.

The dog didn't have a good time going to MNL. It was her first flight and she did poop and pee in her crate and was a mess on arrival. Going back, she didn't eat before hand (we didn't feed her) so just pee in her crate. We did have an absorbent pad in there both ways which really helped. She did have a water bowl, but not sure that did much good. I think it probably just spilled vs. her drinking it. Regardless, she made it both ways without any long term issues.

My two recommendations for NRT layovers:
1. do not change airlines. As long as you are on the same airline on both sides of the connection (and especially ANA), then you don't have to check your pet into Japan, which is a massive PITA.
2. keep your layover short. I think the max time is 6 hours, and ours was less. If you stay overnight, you have to check your pet into Japan.

Good luck!