Detective- What were you doing the day the crime took place? Suspect- I woke up a little late day. When I took a look at the clock the first time that morning, I realized I was running late for work. I brushed my teeth, took a shower, and hurried off to work. I was at work the rest of the day. (chronological order)

Now, instead of putting what he wanted to convey in the chronological order, what if he chose to put it this way.

I realized I was running late for work, looking at the clock for the first time that morning. I had woken up a little late. I took a shower. I had brushed my teeth. And I hurried off to work. I was at work the rest of the day.

If he were to convey what he wanted to convey, putting it this way (the part right above), would it be grammatically correct, and would it mean the same thing?

What other ways, other than putting in chronologically, can what the suspect says be put? I'd appreciate it if you used past perfects more in your example, trying to convey what the suspect says.