Ok, if you want to carb fast, I'd totally change your procedure. Unless you like sediment filled foamy beer.
1. Clean and sanatize keg.(No S*** Sherlock)- Yep!
2. Fill keg with beer. Yep!
3. Pressurize keg with 30psi of CO2 and purge to clear out O2. Yep!
Here's where it changes:
4. Set in kegerator at 30 psi for 36 hours.
5. After 35 hours, purge and reset to 12 psi.
6. Pour about 3 ounces and discard (it'll be sludge)
7. Drink the keg.
I left off about 3 steps, plus the shaking/rolling part. I can see no advantage to shaking, except that you'll maybe have carbonated beer a day faster. But if you can't wait 36 hours to drink (and it'll take that long to cool anyway), then warm foamy beer with sediment might be good.
If you're not in a huge hurry:
1. Fill keg, and purge with co2 a couple of times.
2. Put in the kegerator at 12 psi.
3. come back in 10 days. Pour off the first three ounces. Drink the rest of the keg.