The "slowly rolling into the train" is an issue that has to do with the motion of the train.

Something about the train moving past laterally to the driver seems to make drivers ease off the brake without thinking about it. In the past, it was taught if you were first in line at the grade crossing to put your car in park (auto) or neutral and set the brake (standard). I had to teach both sons about this as it was not covered in driver education here in Texas.

I do not remember the facts around the cause, just some foggy memories from a LEO buddy who went to a car vs train accident school.