I had this problem with an old Huffy that had a hanger just like the one 3Alarmer pictured. I set that side in as far as it would seat and made sure the chain line looked good and then took a rat tail file to the non-drive side. You need to determine by sight approximately where in the dropout you want the axle to sit and then very cautiously take a couple swipes with the file. You will find the metal is really soft and it won't take much with the file before the wheel will seat in the new position. Good luck and keep us posted.
FWIW-on a much nicer bike that I ran into this with I actually line-bored the drop outs. This was much more complicated and I had access to a metal shop at the time.