There is a Costco not so far from the Disneyland area. Not somewhere I’d usually advise, but in your case...
And I really do suggest you approach the volunteer guide associations I posted a link to and start asking if they have someone who can help. You have a much better shot with them than here directly.
On the upside, if you’ve been consuming tamari until now without issue, then soy isn’t a crucial ingredient to avoid. That will help you enormously, at least for this trip.
Have you considered getting yourself a cheap rice cooker? (From about 6/7,000yen for use only in Japan). If you bought yourself one as soon as you arrived you can prepare your own rice balls (onigiri), add other grains like millet (kibi) to make your rice healthier. You could even make quinoa in it. It would make supplementing food with protein and vegetables much, much easier.