I tried the RCG-script. I couldn't use the latest version, since the download-link doesn't work. I used standard V5, which has some problems with FIRS 2.1.3. but I guess these problems only affect industries/cargos.
The problem seems to be the same. I actually managed to keep the cities at a somewhat constant level (very volatile though, it kept shrinking and growing again). But the cities were very close together, which probably helped a lot.
I start wondering if all this behaviour is intentional, and I am just a very bad player, that I find it so hard to keep a city from collapsing. It doesn't feel right though, that people start to leave the city as soon as a train arrives. Personally, I don't know many people who moved house by train.