Army Basic these days is pretty much a joke. It is designed so the average person, male and female, can pass with no previous training. The Drill Sergeants are encouraged to have a high pass rate, so those who should not pass still do.
If you are in decent shape, it should not be a problem. If you are in great shape, you actually may lose some conditioning. But remember, the better prepared for it you are, the better you will do and the easier it will be.
The above posts are right on. Running, marching with a load and bodyweight exercises are what you will see. The army is much more concerned about endurance than it is strength.
I hate to say it, but your current program looks pretty bad for your goals. It looks like a routine geared towards bodybuilding, and that won't get you far. You don't want or need mass for basic, just conditioning.
I am not saying that weights have no place in preparation, just not the way you are approaching it.
Drop the body part splits. If you choose to lift weights versus body weight, do three days a week, full body routines. Squat, Deadlift, Rows, Presses should be the bulk of your lifting, mixed with varitions of pushups, situps, and pullups. With weights, keep the reps higher, 10-20, with minimal rest between sets and excercises.
For prehab, or injury prevention, work on strengthening your core. Back pain plagues soldiers. Also, do spend a little time searching 'shin splints' and you will find some excercises to do to strengthen that area. Shin splints is one of the more common injuries I see.
If you are leaving in July, you have plenty of time to prepare. Don't rush it and overextend or injure yourself. Slow and steady wins the race. Stay consistant and committed. Good luck, feel free to post on this thread or PM me with more questions.
P.S. stay away from steroids and pro hormones. Any gains you might have will soon be lost. What could be worse than rebounding during basic? You didn't ask, but it comes up enough that I thought I'd mention it.