Yes, you can passively the AMD EE CPUs. People have been passively cooling the Athlon 64 X2 3800+ thru 4600+ for a few years now. You can find this info in the www.SilentPCReview.com forums. I've even seen some posts about a few brave souls who were passively cooling the X2 4800+; it's pretty rare though. Those people use massive heatsinks and the case must have good airflow.
The Silverstone LC16M seems to have fairly decent ventilation, but it is only about 6.7 inches tall or about 170mm. That's relatively short for a large heatsink. I use a Scythe Ninja to cool my E6600 and before socket AM2 hit the market, it was one of the most widely used heatsink to passively cool CPUs. Scythe Ninja (rev. B) is compatible with socket AM2 now, but it will be too big for your case. It measures about 150mm tall or about 5.9 inches. But it needs to sit on top of the CPU so the approximately 20mm clearance is definitely not enough.
The limited height also prevents you from using the Tuniq Tower which is also a very good heatsink to passively cool your CPU. It is slightly bigger than the Scythe Ninja.
A quick recommendation would probably be the ZEROtherm BTF95 CPU Cooler. I have not done any research on this product. However, this heatsink is quoted at 128mm or slightly taller than 5 inches. It is almost entirely made of copper and is a better heat conductor than aluminum. In my opinion this is probably your best bet, unless you do your own research.
ZEROtherm BTF95 CPU Cooler:
http://www.newegg.com/Product/Product.asp?item=N82E16835887001