A general rule of thumb is to use filler rod that is the thickness of your material or less. This is because it might take more current to melt the filler than the base metal. What you describe is possible, but it will require skill to pull it off. I would get some .040" filler to make things easier. But any kind of thin welding takes practice. If you concentrate the heat on your .062" part, add the filler there, then wash the puddle up to the .030" part, you could produce a good weld. I would say start with .125" material, then .062" before trying .030.
Long arc, short arc, heliarc and in-the-dark!