Also, don't think you have to take up jogging in your full gear in order to get endurance. You can challenge your cardiovascular system without having a wind-sucking experience. However, jogging in full gear is not a bad way to learn how your gear will perform. But I would advise to keep the distance limited, but with a mix of flat and rough and rocky terrain. I would also advise you to do certain things like isometric squats and pushups. Hold these positions in a way that mimicks things like leaning, crawling, etc. Crawling for a long distance in various positions is a good idea too as long as it is steady and consistent.
Don't underestimate the need for endurance training. It will make or break your ability to stay in the fight. There is a reason the SF selection puts candidates on long endurance courses. Endurance in all aspects is what you will need physically and mentally if you are going to perform at your peak when the time comes.
You don't need to look like Hulk Hogan or Dwayne Johnson in order to have more than adequate strength to perform. My advice would be to start with just your bodyweight until you can perform the pushes and pulls slowly 10 times with ease. Then I recommend doing them with gear on. Add on the gear in increments and let your body get used to the load. Again, we are aiming for true strength, not endurance or power. Smooth and controlled manipulation of heavy weight will cause maximum muscle recruitment and therefore, more overall strength. Do these lifts and movements right, and with great patience in order to get the fastest results.
My advice is to only intermitently work on your strength training. Get to the next strength level and then build around that with your endurance and power.