Did you look carefully at the Emotiva BPA-1 link? I believe it represents everthing you want...including the fact that it's an integrated amp...just plug in your source. And with it's feet removed, it will make your 5" max size requirement. (I'll double check mine, if you wish.)
Emotiva gets rave reviews. It's rear cooling, so you don't have to worry about top space. It's stable under 4 ohm speakers. And it's pretty darn cheap. And let's not forget....it has those lovely cobalt blue surround lights.

IMHO, it's one of the most versatile, coolest little amps around.
What is your objection to it as an answer to your search?