About 8 years ago I was doing my bachelor thesis in the field outside a small city in Northeast China, and I saw the K19 train passing on a rail way not far away - the train wagons were arranged one in green, the next in brown, taking turns, with "Beijing/Moscow" printed on the brown coloured wagons. It was a beautiful scene at dusk. Solemn, nostalgic and serene.
The K19 takes an alternative route from the one you took: Beijing - Harbin(my hometown) first, then the train goes out of China from north of Heilongjiang province (part of so called "Manchuria") to Russia, not touching Mongolia.
Maybe one day I will take K20 home 🙂