preserving leftover cooked rice from Chinese takeaway for processing in a cold salad afterwards
We often do the same thing, saving the rice for another use the next day. Or sometimes I will ask my husband to pick up takeout that I can heat up for lunch the next day. Here's what I recommend.

Immediately upon returning home with your takeout, remove the rice from the take out container, placing in an equal size airtight container. E.g., if you have one pint of rice, place in a pint container. Don't break the rice apart any more than necessary. Press the rice so that it holds tight together in the container just as it was when you removed it from the takeout container. Put the lid on right away. Refrigerate to store.

By placing in an airtight container right away, you are shortening the amount of time that moisture can evaporate. By using the same size container there shouldn't be an excessive amount of airspace in the container.

I follow this procedure and the rice comes out the next day just like it went in, still moist. Plus it doesn't really require any excessive time or effort.