This one isn’t a personal recommendation but “Shabu Yo” is on my radar as one of the cheaper “all you can eat” shabu shabu restaurants.
Price varies by how much meat you choose and what time of the day you go (or if you want a 60 minute or 80 minute plan), but the gist is that - at lunch time - you can get unlimited quantities of vegetables (as well as noodles and a few other ingredients) from 1,000 or 1,200yen upwards.

Map showing locations
https://store-info.skylark.co.jp/syabuyo/

A page showing what is available, for how much and the times (as well as drink options)
https://www.skylark.co.jp/syabuyo/menu/index.html

The how to guide:
https://www.skylark.co.jp/syabuyo/enjoy/index.html