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I get that you're putting in time and not getting the expected results, but it's important to know that it's all about how you use that time. If you push yourself properly, you can get a great workout in way less than an hour.
Stronglifts 5x5 is a bodybuilding program, and is fine for training to lift heavy weight, but you need to be training to be fast, athletic, and durable, not big. Things like weighted lunges and overhead presses will help more. Don't sit and rest between sets, find something else to do while the first thing recovers. Jump rope was mentioned and is a good example.
I agree with your friend, especially with the 2-month goal in mind and your current status. Beginning where you are, I would say that you should start with body weight routines and work in weighted movements as you progress. HIIT is a great way to include cardio in bodyweight movements. Try the "12-Minute Athlete" app, and do 1-3 of the workouts as a session. I really like that app.
You also need to build what's called a cardio base so that you can train to run fast with endurance. You should be aiming for around 20-25 miles per week, and mixing sprints in with your steady-pace runs. On days that you do sprints, try doing bodyweight movements between sprints, i.e. a set of pushups or lunges. Rest less. Check out Stew Smith's series of running programs. There are also other ways to get cardio than running if your legs/shins are hurting; hop on a stationary bike and look for the interval program.
Probably the single fastest way to drop time from a PFT is to run longer sprints, like a series of 400 or 800 meter runs (8-10). If you don't feel like your chest is about to explode on sprint days you're doing it wrong.
To add pullups quickly, look up the Armstrong pullup program, or the Recon Ron program, and stick to it religiously.
There's working out, and then there's pushing yourself to improve.