The "heavy QRM" between numbers is a mode called RDFT. They send files with encrypted text which are partially identified by the number sets. Those files likely contain the real messages being sent, if real messages are still being sent by Cuba.
They are definitely transmitting from Cuba for North America. I'm not technically adept enough to describe how, but they know that it's coming directly from Cuba.
One fun thing to listen for is errors, most often Windows startup sounds and Radio Habana Cuba audio. At times HM01 audio will appear on RHC frequencies as well.