Hi Colum,
Reading through the User Manual, item 4. of the "Converting an Idea to an Investment" section on this page states that these boxes are checked by default OOTB, and that you will need to clear these boxes manually so that the budget information is not copied from the Idea when its converted to a project.
I checked in studio if there is a way to change this default, OOTB behavior, but could not find a solution. Perhaps another technician is aware of a method for achieving this outcome? Maybe this can be achieved with BPM, not sure...