My favourites off that menu would be eel in any form (it's seared, so not raw, in a sticky sweet sauce) kabocha korroke, salmon sashimi, scallop sashimi, salmon roe, nasu dengaku, ebi tempura, agedashi tofu, anything with gomae dressing and tsukimono. I love anything sesame flavour.
If there was sea urchin gunkan (uni), that's my absolute favourite.
Bao buns r ok (bao means bun in cantonese, so they are called bun-buns?) But they ain't Japanese. Then again "cha siu" is Cantonese too. Means roast pork. Ramen is chinese too, derives from the words lei mein. When I was in Japan a lot of the ramen restaurants were loosely chinese styled even down to the big ramen bowls and pottery spoons with traditional chinese patterns on them and they call it the chinese words "cha siu" too, whereas in japanese it could be something like buta yaki . Isn't it interesting, the mix of cultures and cuisines!
Anyway I digress, to fit more in I suggest to go easy on the rice based sushi rolls and go for more sashimi and side dishes followed by a bento box which will have rice in it anyway.