If you're going to be adding in extra workouts and trying to increase GPP, do it slowly. Start out with very easy extra workouts and once you know you can recover from those AND you're lifting, then you can start increasing the intensity. Increased GPP will allow you to have faster paced and more productive workouts and help you recover more quickly.
Westside do TONS of extra workouts that will only last 30 minutes or less, they will just be something like 3 assistance exercises done lighter for higher reps all one after another. Those type of workouts increase work capacity as well as helping your lifts. Sled dragging isn't meant to be done extremely heavy, it's not meant to increase 1RM strength.
Right now, dragging a sled might sound crazy to you and like you won't be able to recover but once you increase your work capacity and GPP, you'll be surprised how often and intense you're able to train. Also, yes as you get stronger it is more difficult to train with the same volume as a new lifter does. This is because you've tapped into more of your body's strength potential than someone who isn't as strong.
Anyway, you don't need to immediately start intense sled pulling to increase GPP. Do something easy like walking for 45-60 minutes at night and finish with some ab/core work or something. You really will be surprised how quickly your body will adapt to these extra workouts and how much of a positive effect it will have on your lifting.