I suspect that the combination of the IR-resistant film and the shades was more than additively worse than either by themselves, because the shade tries to send heat back out through the window, and the low-E film was fighting against you. If the shades are actually any good at reflecting radiated heat, then you don't WANT low-E film, you want the light to come in, bounce off the shades, and bounce back out, without even noticing that there was a window there.
Do you have window screens on the outside of the window? Those would help, and you should get enough airflow through the screen to keep heat buildup from being a problem.