I would go LH and hope that F opens up on the 2nd flight. Your decision will depend some though how much you value the additional 20k miles. If you have plenty go with LH.

Not sure what the 'new' NH cradle seats are. I was on a NH 767 recently from HND to PEK in C and it was not that comfortable to sleep. But the seat didn't look new to me so might have changed. Same seat on a different NH 767 from HKG -> NRT.

I would go LH for the F terminal or the F lounges. Either one are fine and usually quite empty. Also nice showers and a good place for a sit down meal. The NH lounges are not great, neither is the RCC at NRT. Even NH's first lounge is not that good in my opinion.

LH arrives 1 hour later though so that is a draw back.