Here's a thread on my diff cooler install.
MA Motorsports Diff Cooler Install
It doesn't fit with the stock muffler or anything like the stock muffler. If your exhaust is like the FI with twin cans. It will fit.
When I did my install. I also installed a Z1 diff cover and an OS Giken diff. The OS Giken diff uses diff lube that cost about $70 a liter.
With the Z1 diff cover and the diff cooler. It takes about 2.5 liters.
With the diff cooler pump and fan off. The highest temp I've seen on my Diff temp gauge was 270F. Turn the pump and fan on. I can watch my diff temps drop to under 200F.
When oil or lube get foamy. They don't lubricate very well. The bearings will lose their lubricating film and run dry. This is what may have happened to you.