Just recently I noticed how great I feel when I excercise in the morning, and I finally bit the bullet and joined a gym. The thing is, I work 6AM-6PM, and in the fall I'll have school after that until 9pm. So only options are before 6AM, or after 9pm. I joined the Edge and they open at 5AM. All told, I gotta warm up, work out, stretch, and shower and be out of the gym by 5:45 to make it to work by 6. Which doesn't leave me tons of time lol so here are questions.
I'm gonna be strength training primarily. Is getting a legitimate workout in that amount of time realistic? plan was 5 minutes of warm-up, 30 mins of lifting weights, 5 mins of cooldown/stretching, and a few minutes for a small margin of error, and shower. I'm worried that the warmup and cooldown/stretching periods are too short though.
plan is to do less per day than some recommend. So instead of like an upper body day and lower body day, I'm thinking of an arms day, chest day, back day and leg day. And then I'll work rest days and probably a cardio day into that. This way, each day I'll have fewer muscle groups to work, and thus need less time. If need be I could work in a workout after 9PM, but that's pretty late. I'm just lookin' for suggestions because I really don't wanna get into this and lose motivation. So if anyone can help, I really appreciate it

Just some background info also, like I said I'm not tryin' to lose weight. I'm 5'5, 165-170lbs. I work on an oyster boat, so it's relatively hard physical work all day. That's the only reason I'm in pretty good shape. It just gets easier the stronger I am, so if I can get healthier and make job easier, why not?