Apparently that board really doesn't do well with quad cores at all. It's not really an issue of the phases heating up, but that the board cannot provide enough power. The single four pin connector just isn't enough. Even if it was, though, the VRM structure just isn't meant for that type of amperage.
As far as I can tell, there isn't really an ITX board made for clocking anything more than a dual core.
EDIT: To clarify, it would do fine with a quad at stock, but overclocking is where it would struggle. When I needed a semi custom heatsink for my 4890 VRM, I took an old heatsink and dremeled it to shape.
EDIT2: I actually considered doing something similar with mine (H55M-UD2H) when I had it. I was just going to make a cooling plate out of some aluminum stock that I had. I just used a piece or art foam to get the sizing down. I ended up selling it before I did it though.