The last thing you'd want to do on such a tight schedule is trek all the way to Toyosu for a sushi breakfast. Daiwa, Dai, and the place you mention above (
Dokoro Yamazaki) are all in Toyosu. They're passably decent sushi, but not worth the trip to Toyosu on such a tight schedule. (And possibly not worth the trek to Toyosu under any schedule, to be honest...)
There are no "delicious" sushi shops open for breakfast, in my opinion. You're much better off having sushi at lunchtime. Personally, I'd do that instead of the whole "get to NRT at 12:30 to enjoy
the F lounge" thing. But if you must absolutely have sushi for breakfast, I'd recommend a place like Sushi Dokoto Tsukijiya in Tsukiji - it will be comparable in taste to places like Daiwa, but Tsukiji is easy to access and centrally located, so you can have a nice walk around Ginza or Shimbashi afterward.