The footprint varies quite a bit between different Toto models...maybe, if there's one that would cover the flakey tiled job they would accept, and you paid the difference, they may go for it...worth checking rather than taking something with known deficiencies.
Another possibility is to crack a few tile out and pick something that complements the already installed stuff such that you could then install any toilet properly. The likelyhood of finding matching tile is probably slim.
Thanks, Jim, for your good suggestions. The attitude was, "We're more than happy to replace your toilet with what we use now, no problem, and problem solved. Next." They really didn't want to discuss it, I guess because they figure they have a solution and don't want any "help". In a 500-unit building, I'm guessing that they want to have one size fit all as often as possible. The chief mechanical guy told me, nicely, "We haven't had any problems at all with the Gerbers" (I guess he meant with respect to clogging), and seemed more concerned that I understand that the toilet had a normal-size tank and wasn't low-profile. Because I don't know the dimensions of the under-the-AS cement, I don't know what to propose, unless, of course, I can find something that covers everything that the AS covers, which is actually a good idea. If I can do that, I think I have a shot. Otherwise, this particular group is just going to say, "No." Also, a skirted Toto ain't gonna fly, because I know they have no intention of drilling holes for the Unifit into the expensive-looking red marble that they used on the bathroom floors, which probably also explains why they didn't just add sections of tile in the area that was untiled. (FWIW, another stupidity is that this modern building has 14" rough-ins, so there is substantial wasted room behind the toilet in the already-small bathroom; a Unifit could have helped that, but because of the manner in which the bathroom flooring was done, in this case I guess it would just guarantee an additional area of exposed cement.) So unless I can find the perfect footprint for a replacement (and I will try), I will probably end up having to take what they're planning to give me. I do respect, and don't envy, the operating guys in a building that size who have to figure out how to work around the hand that they have been dealt. I just wish I had raised my concern a couple of years earlier when they were installing Totos, which I would have done if I had known that they were so willing to do a replacement. And I should probably be relieved that the new replacement wasn't a Kohler with the Ingenium flush (which I had begun calling the "Stupidium" flush before I finally ripped the thing out and replaced it with a Drake).