You carry your weight well because you lift. You look kind of like a power lifter instead of just a fat guy. You can still drop weight. You’ll look better with every pound. Police work is toxic. The stress and hormonal responses to stress causes the body to store belly fat. Read up on the body’s stress response and cortisol if you’re curious.
The leaner you are when you start, the better off you’ll be. You are in a better place to lose weight now with your 9-5 job. I’m assuming it doesn’t have multiple adrenaline dumps each day.
If you never run more than 2 miles then train for that. Your 5k goal is a good start. Google “Beginner Program for a 5K” and you’ll find plenty of programs.
Your academy sounds like it’ll be like my second one. We did minimum PT. We had to run 1.5 miles in 14 minutes. We might’ve run further than that once but definitely not more than that.
Maybe this will help you grasp what (I think) you need:
An officer needs strength and strength endurance. You might run for 30 seconds to catch a suspect and then have to fight him once he’s on the ground. You need general endurance - not so much the ability to run far but the ability to stand/walk for long periods with 30 extra pounds in hot weather. You also need to be able to do what I just listed above on those days.
To train for this I think weight lifting with short rest is good. I think sprint intervals are good. I like circuits with weights or without. You might like Built for Battle since you like to lift heavy-ish. And some steady state cardio on occasion is beneficial.
To be honest, CrossFit type training is probably ideal for cops but I don’t like just doing the WODs. Some of the movements hurt or I just can’t do them (hand stand walks and hand stand push ups, for example). I’ve started building my own little WODs that let me lift and push my conditioning a bit. I can build them however I want to meet my needs (or wants). The important thing is that I’m ready if I have to fight for my life someday. Strength will help, but conditioning is going to be the key. Recovery is key. I may not be able to fight for a minute straight but I can probably find a way to stall for a few seconds. If I can recover enough to go hard again then I can stay in the fight.
It sounds like you’re on the right track already. Add push ups to your training. Train your abs and core both statically and dynamically. I’d guess that your squat and deadlift numbers are limited by your core right now. I’m 6’4" and 240 right now and I pulled 545 in June. Based on your photo I’m guessing you’re leaking power in your core or your technique is off. But I digress…
Back to your training. Choose your reps on the bodyweight circuits based on your abilities. I’ve been doing 20 walking lunges (10 ea), 15 push ups, 5-8 pull ups, and 10-12 reps on an ab movement like lying leg raises, v ups, or ab wheel rollouts. There are a couple CrossFit WODs that do 5 pull ups, 10 push ups, 15 BW squats. One is as many reps as possible in a specific time and the other is a total number of rounds for time (hell, I might try that today since I’m training at home).
I think I’ve managed to cover most things. Sorry if I missed anything or something doesn’t make sense. I’ve been distracted while writing this.