I know that on paper, the True Muscle Trainer doesn't seem like a ton of work. But you need to let that go. More work does not mean better results. Smarter, better work means better results. High-volume training can work in the short term, but if you want long-lasting results, you're going to need smart programming that will challenge all aspects of your fitness and allow you to rest enough for proper recovery.
If you do this workout with the proper weight and intensity, you should feel fatigued when you're done. But, you should have enough energy left in the tank to attack the 1-mile run afterward. I know a mile run isn't fun, especially when you're doing it for time, but I think it's a fantastic way to test your fitness and will be a great way to measure how much better you get over the next three weeks.