I'm also a shower in the Mikvah person, although when I was a bachur I would sometimes abuse the shower at home. LeMaaseh I shower more or less with my eyes closed by default. Here in Israel, most people turn the shower on for 30 seconds so that their body is wet, and then lather themselves up and then rinse off. so I start with my head and my face -which means that my eyes must remain shut if I don't want them to get full of shampoo and soap- and then continue washing the rest of the body (BTW this is the right order halachically and kabbalah-icly concerned) washing right, left, then center excluding the groin area . Then I let the hot water pour down and rinse me off, and I come out squeaky clean -physically and spiritually. When you do things in a ritualistic fashion, it sort of helps you stay focused on what you're there to do...get clean!
Besides, you can try and commune with Hashem in the shower as well! You can wash your head and think: 'G-d, I can wash my physical head -but only you can wash the filth out of my mind -I'm doing what I can -please do what You can...' and the same for the rest of your body...Just stay focused: G-d I'm in the shower to get clean physically...help me get clean spiritually...
What's wrong with your original idea? I.e. Disconnecting your mind from everything except washing your body and hair, while trying to be mekabel on yourself not to place your hands or look at the entire crotch area? The suds and water get down there and do their job without your hands.
It's alot better than skiing, snowboarding, or geting a 'tan'!
Hang in there,
Ben Durdayah