I dropped 20 pounds over 6 months using mostly the Simplest Strength template. I lowered my supplemental lift TMs because on 5 week, I started failing on the 3x10s. I suspected the calorie deficit had a bit to do with that. My strength gains were slow, but steady. Every main lift went up in the process. I even hit a PR at my body weight in the press at the end of the 6 months.
I didn't do anything exceptional in cardio. I sprinted twice a week and took walks most days. (I get 3-4 miles of walking at work). I slept and I recovered. I think the reduced volume of SST helped (me at least).
I think the biggest key was that I took a slow approach to it. I only slightly reduced calories. My deficit was less than 300 per day, and never more than 500. That and recover, recover, recover.