Invisalign can do some uprighting, however it sounds as if you have more major instabilities in your bite than just a minor tilt of the molars. You mentioned in your story that it's your 12-year molars that are missing. The 12-year molars are numbered #2, 25, 28, and 31. I just want to be sure it's your 12 year molars (if so, there should still be a molar in front of the space as well as behind). Then the molars behind the space would be your wisdom teeth and the molars in front of the space would be your 6-year molars (numbered #3, 14, 19 and 30).
If this is the case, I would say the best treatment would be to remove the wisdom teeth and place implants in the 12-year molar spaces. If that is not the case (and it is actually your 6-year molars that are missing), then I would recommend orthodontics (braces with or without mini-implants) first, followed by implants to replace the 6-year molars.