This place (6 Eu Tong Sen Street #03-88, 6327-7887) is run by the people behind Tampopo. It's been around for a while now, but I kept forgetting about it until I finally came down here today and noticed that they were doing a sukiyaki lunch special for just S$12.80 (US$10). This was a considerable savings against their normal prices of about S$30 (US$24) or more, even if this version excluded things like rice, which I had to add separately for S$3 (US$2.30).
It turned out to be a lot better than I thought it would be. Part of it was simply because my expectations were very low, based upon what one could get at Tampopo proper. Part of it was also a sense of futility after many failed attempts to get a decent experience elsewhere. But the ingredients here, like the tofu, were better than I thought they would be.
Too bad they only offered a sweet sukiyaki broth at this price though. Shabu shabu was available, but only on the regular menu, whose prices were multiple times higher than this. At least this experience was encouraging enough that I'd be willing to come back again some other time for that, hopefully with someone else paying for the meal.