So, funny story, in the beginning of 2022, I came up with the exact same scheme discussed in this thread. ...
I've spent the last year implementing it, so just 10 years after the OP, you can finally try it out!
The binary, written in Rust, is called
ord, and the code is on GitHub at
https://github.com/casey/ord.
Sounds like a fun project, but I don't think the idea has any practical use because there is no
association between the satoshis in the inputs and the satoshis in the outputs.