I'm on the opposite side of the dining spectrum to you, so the only places I could imagine that would serve you well in this regard are those that specialise in Wagyu or Kobe beef.

Also yakitori places - which specialise in flame grilled chicken pieces.

Err... perhaps Wendys or Macdonalds and throw the bun away.

Best sensible suggestion I can give you for once you've exhausted your shabu shabu options (which will drain your wallet - you saw one of these near the end of Lost in Translation where the thin slices of beef all looked the same to the rude and ungracious characters) and have grown tired of the taste of grilled chicken pieces is to visit the basement floors of Departments stores which is where all the food is kept (depachika).

They are like massive delis - you can buy raw food and ingredients there, but you can also buy a great deal of pre-cooked goods. Some of these are in pre-packaged 'bento' boxes, but in lots of cases each component of a meal is packaged and can be purchased seperately.
Even with the concessions where the staff serve hot food in front of you, you can pick and choose elements individually - just make it clear that you don't want rice or whatever else it is you don't eat.

Even if you think you don't like fish, Tokyo would be the place to find out once and for all if you really truly don't like it (but prepare to splurge out if you want to taste famously great sashimi - don't decide it's no good after a visit to a conveyor belt joint).

A shame you won't eat fish. For many Atkins devotees, Japan must be a dream destination....

EDIT to add - I just re-read your question. You don't actually say you don't like fish, so forgive me if you are happy eating it. If so, remember that you can also buy ready made sashimi in the Depachika too - if you keep it in your hotel fridge, it may make a suitable breakfast for you the next day. (Sorry, but my imagination completely fails me for what people on this diet do to keep it up. Well, it doesn't entirely fail me - there are lots and LOTS of supplements, drinks and medicines around for those who want to keep themselves regular or require relief from 'bloating'. Once you know what you're looking at, the store shelves are packed with a whole range of these dietary aids.)