Are you focusing on max strength, as 5/3/1 is known for, and fat loss simultaneously? I have never done this but with my body type exercising for strength would not be possible without tons and tons of food, quality food mind you, and I barely gain any weight, though i lift primarily for strength and care not much for hypertrophy. It seems you have many goals, which is good, but fat loss/muscle gain/strength gain all optimized at one time is extremely difficult.
You should check out Chad Waterbury's book Huge in a Hurry. This book was golden for me when I worked for hypertrophy and it never failed to build quick, quality, lean muscle all over the body. He also has a workout called Get Lean in the book, which he recommends anyone trying lose fat start with, because it's easier shed fat THEN build muscle, rather than vise versa.
All the workouts in the book are 3x a week full body workouts, utilizing mostly compound movements. Plus the science behind his methods are solid and concise for optimal training performance tailored to specific goals. Check him out on T-Nation. He has posted much of worth