I was going to recommend Scarlet Heart, but you've already seen it.
I can't think of any other Asian dramas to recommend, but if you're interested in Czech TV, then I have two recommendations for you. Both are good, but they might be hard to find. I'm not sure if they're available on streaming sites.
Arabela (1979) is about two princesses who travel from a fantasy world to the real world.
The Visitors (1983) is about a group of 4 scientists from the 25th century, who travel back in time to the 20th century. One of them is a woman in her 20s, but she's not a princess.