You know, if you're going to be busy for a few weeks just hang this project up somewhere and let those wrinkles (which I can't see) hang out. You may be surprised.
Another thought, about 6 years ago I was using a spary product that eased out wrinkles without ironing. :D It was my favorite product at the time but I can't remember the name of it. I'd spray my shirts and give them a slight shake or tug and the wrinkles magically disappeared. Neat!