The problem is that Rammus is a tank. While that might work in theory, in SR, where does rammus go? He goes in the Jungle, where he gets modest farm. He can't really top, mid right?
Due to this limited budget, and the need to be pretty tough, he just doesn't have the budget to go Tanky AP which is what you suggest.
A Cho Gath can pull this off because he gets a lot of free life (900) plus decent base life as well. And he has multiple high AP ratio spells.
Your powerball is more of a mobility thing than an actual attack spell. Your Ult is very strong but Living Longer tends to make it do more damage over boosting with AP. (see fiddlesticks)
Rammus also wants improved cooldown reduction for faster Taunts and more available Ults.
So I would not recommend this as a viable approach. You might try it in Dominion for Funzies though, since the farm limitation is mostly removed.