While I'm a big proponent of body recomposition using barbell training, the increase in BMR you state is not conclusive in studies.
"Anaerobic exercise — such as weight lifting — builds additional muscle mass. Muscle contributes to the fat-free mass of an individual and therefore effective results from anaerobic exercise will increase BMR. However, the actual effect on BMR is controversial and difficult to enumerate. Various studies suggest that the resting metabolic rate of trained muscle is around 55kJ per kilogram, per day. Even a substantial increase in muscle mass, say 5 kg, would make only a minor impact on BMR."