I sometimes believe we tend to overthink issues related to weight training. Years ago, admitedly before alot of the more precise information we have today was widely available, I would use 45mins. of tread mill or bike on my off days AND after training sessions, in order to cut body fat.
I always lost significant amounts of body fat while simultaneously gaining muscle! So, I sometimes believe we try to be too careful–to tweak every detail too precisely. The human body can take a lot of stress/volume if other factors are optimized (e.g., diet, supplements, rest, etc.).
Now, having said this I need to mention:
A) I was a lot younger when I did this (about 10 years–jesus!).
B) I was always starting at fairly high body fat levels. Research has demonstrated that those starting at higher body fat levels during dieting lose less/no lean mass. Dr. Connelly postulated years ago that those with over 10% body fat can pay the “caloric expense” of building new muscle from their body fat deposits. This was revolutionary–at least in the popular bodybuilding literature. Thus, he said, you can both lose body fat AND build new muscle IF other (primarily nutritional) factors are in place.
C) I always used a MRP that had high levels of casein protein in it. Research has demonstrated for years that casein has unique anti-catabolic properties. It preserves lean body mass by increasing total nitrogen retention better than whey–especially useful during dieting.