Coach Sonnon worries about useful strength. The least useful or lets say least complex is machines that target one muscle. Then are free weights. Then Kettlebells. Then clubbells being the most complex. To make it short....yes...CST is teaching you strength useful in more different ways. There are too many guys out there who can lift all kinds of free weight. But cannot lift their own body weight. Can't do a pull up...etc.
I don't have any of the Tacfits. I do know they make it easy to understand a good schedule and workout. The kind of workout schedule that CST hopes a person would do.
Running is something great to do. I would do lots of mobility of the hips and lower spine to make up for that overcompensation.
No matter what. Lots of joint mobility and range of motion training does you wonders. Yoga is great. This stuff goes along with your weight training.
I don't think you're cocktailing right now. Throwing in a Tacfit program along with what you're doing would be.