Try putting the heat sink that was used for the memory and vrm from the stock cooler and just put the zalman fan on after that. Basically remove the fan from it and the shroud and you left with that black aluminum heat sink see if you can get that on first then just put the zalman cooler one hehe.
The reference stock heatsink + fan assembly is just one huge chunk of metal, heatpipes, and plastic. There is no seperate pieces for ram or VRM.
Here's pictures of the 5870 itself, the top of the HSF, and the bottom of the HSF. Yes there is white thermal paste on some parts because I had to take it apart once already to try to fix the fan (thought it might have been out of lube or something. It's just plain ol shot)