"Once you or I have a self-hosted compiler, if it can compile to a platform, it can also run on that platform."
In theory yes, but it wouldn't be a good idea for jasper because it is a relatively thin layer on top of javaScript. So a backend for a different platform would have to emulate a lot of JS quirks, which would be complicated and produce slow code.
So if you want to make a cross platform language, it should be a thicker layer on the first platform from the beginning.
"Nevertheless, I think I'm still headed in that direction."
Always make backups of your compiler binaries or don't overwrite old compiler binaries so in case of a bug you don't end up with only one, broken, compiler binary.
