After some weeks of headbanging and waiting for new magnetometer units to arrive (which also didn't work) I have finally discovered the following.
The common modules sold on fleabay, although marked 5883 are NOT HMC5883Ls but instead something called a QMC5883L! (mercy...)
I have found working Arduino code for these, hopefully at some stage we can incorporate it in the Lua codebase too, as these modules seem to be by far the most prevalent.