I've spent just enough time studying that language in the last few months that I am calling it "Zhongwen" in my head and find it hard to write "Chinese" instead of 中文.

Certainly if Chinese people met English speakers when English speakers didn't have a writing system they'd find a way to write English in Chinese characters the same way they did for Japanese circa 950AD and that they've done for several languages unrelated to "Chinese" that are written with those characters.

The effort in that article goes in the direction of making something regular that works a lot like "writing Chinese in Chinese characters" but it seems to me more likely to go in the more complex direction of preserving Chinese semantics at the expense of phonetics that happens when you "write Japanese with Chinese characters".