Really great advice so far! I found this link on a bootcamp design thread. The exercises and drills might be what you can expect to experience.
After talking to my Sgt. son and giving him your stats, he feels that you will do fantastic. He reminded me to tell you that they count pushups differently. Down-up-down-up=ONE. Good luck, keep your head on a swivel and your mind on your job. As for the last week? Spend it with you family, you will miss them more than you think. (That is from my son as well) He says if you can do 82 pushups in 2 minutes you will get max scores on your pt test. Army does not do pullups. Also, if you are a big muscular guy and have a combat job, ie, infantry, scout or tank, you will lose a lot of muscle because “that’s just the way it is.”
Your push-ups, pull-ups, sit-ups and running are great. With those numbers you shouldn’t have any problems. As you know there will be much more drills and evolutions involved in your basic training, but I think you are in a good place as far as your upper body strength and running goes.
For rucking, get a backpack and put in about 50lbs of weight (40lbs if you haven’t’ done any rucking before and bricks would be my first choice) and go for longs walks at least 4-5 days/weak. Chose all type of terrain (including water, hills, dirt roads, sand and concrete) and start walking. It will be some discomfort in the first few days (especially in your upper and lower back and feet), but it will be a good conditioning training for you. Take good care of your feet because you don’t want to get blisters that will make your basic training a painful experience. When wearing boots, use thick and dry socks as much as you can and make sure you have the right type of boots (you can start with athletic shoes and slowly switch to army boots). If you need more tips/help please feel free to email me. Four weeks out is not that much time to get your rucking conditioning to optimal levels, but it will do for basic army boot camp training.
For whatever it is worth I would be doing a lot of rucking (with 50lbs+) and covering distances of 40 miles or more each week would be the norm. Also running and strength training (particularly push-ups, pull-ups, core work) would be part of my training regimen as well. But, just like I asked you in my previous answer, this program would be based on my current physical conditioning level and the parts I would need to improve. Your mentality and training should be closer to that of a Special Forces level than a regular army. All of the above training suggestions should be done in a full army fatigues and boots.
I hope this helps and good luck to you!