This, remember the heavy bag can be a fight sim - not just a place for conditioning or repetition. Something more technical that I'd add is when you throw body punches you tend to punch down and/or lean forward. Bend your legs slightly more when you go to the body so you don't have to open yourself up as much defensively and risk your balance.
Every time your left hook landed on the bag, your right foot was in the air. You aren't getting your weight turned on the left hook. Done properly the body weight is on the right leg when the hook lands. You are keeping the weight on your left foot. Then you don't get your weight behind your right hand because it is already on your front foot. That is a detailed way of saying that your punching technique is off.
I agree with both of you. Leaving your weight on the left/front foot when throwing the left hook is the same as leaving your weight on the right/rear foot when throwing a right hand. A person might be strong enough to still hit hard, but not as hard as they could if they shifted their weight. There are lots of advantages to keeping the elbows in. When your elbows rest against your body with the elbows bent, the hands naturally stay up. When the elbows are in, it's more likely that your body will be behind your punch instead of just arms and it's probable that your punches will be more compact. The elbows give you some protection from body shots. When your opponent hits the elbow with his fist, the fist usually gets the damage. Same with the inside and outside of the forearm when it hits the elbow.