This is great advice. I've dealt with the same issue and for me, it's all about trial and error accompanied with reading anything I can get my hands on (including the internet). This is only my 2nd year ever playing golf in my life, but I've played baseball for a good portion of my life, which is what I attribute my power to. Anyway, this advice is right on track with what I've seen other places, and experienced success with myself. I've battled a steep swing that can still rear its ugly head from time to time.
I'm left handed, but the principle still applies. I've tried a lot of different things and stick with what works. For me, it was casting a bit away from my body on the back swing, focusing on coming down from the inside. I thought to myself, "I probably look like Furyk right now, but who cares? It's working."
The funny thing is, though, when I looked at my back swing in the mirror, it was exactly how it should've looked. This proved to me that my perception isn't always accurate. And since you can't overload your mind with things before you swing, I keep it to usually 2 things before I start my back swing.
1.) Keep posture
2.) Finish high (hands of course)
That's usually what it is, but since some days are better than others, I may replace one or both of them with "Keep your bottom arm straight," or "Drive the ball into the opposite field gap."
I promise you, that will work. I'm a 23 handicap, but that's because my short game is atrocious. Keep it simple, brother.