I did it!

I could not find any other display online, that would have worked. Even the 192128C I ordered was the last one in that shop.
After beeing sure, that the replacement display assembly I have would not be compatible, I had no other option but to try to swap the LCD itself to the old controller module.
I used a hot air gun set to 200°C, the actual temperature was more like 150°C. Maybe a little more heat would have been better, but I wanted to start at the low end.
I managed to remove the new LCD with it's flat flex cable intact (see photo). The glue sadly did not really come of, but instead stayed on the PCB. But as can be seen in the photo, the cable was only glued in on a ~3mm wide bar, so there was still some "fresh" glue left on the very edge of the cable and on the inner side.
Do NOT get the idea to cut some of the flat flex away so you have a "fresh" and with a lot of glue. There is no mm spare length in the cable, if you make it any shorter, you won't be able to get the LCD into its correct position.
After cleaning the pads on the original controller PCB, I aligned the pins under the microscope and stuck it down with some capton tape on both sides. I heated it up again and pressed down with flat screw drivers and a piece of rubber. I went along all pins multiple times. It did not work perfectly the first time, since there is not really much glue left and maybe because my heat was a little too low. But after a second go, I managed to get all connections done.
I quick test revealed, that the LCD survived and has no dead lines or colums. I did not really think, this would be possible.
The connections on the hot-bar are now of course not nearly as strong as they were originally, so I don't know, if some might fail in the future, but for now, it's 100% working!
After this repair, I finally peeled of the last piece of film from the front panel, after the unit was in use for over 13 Years ^^