SRAM Omnium crankset

Hey there,
I thought this issue would fit in this thread.

Originally, I ran the regular Sram Omnium cranks with default Sram BB. After several thousand km, I'd want to upgrade to a better one. So I got the Chris King GXP (road); this version: http://www.bike24.de/1.php?content=8;navigation=1;menu=1000%2C4%2C23;product=36500;lang=2 (BBB4R)

The problem after installing is the following:

1. Spider hits the chainstay
   
2. Overall much play in almost "any direction", even when the crank bolt is torqued completely -> there is a very noticable gap between the external cups and the crank arm
   
   

Can I fix this by using spacers, somehow? It seems like the spindle is "too long" with the new BB, so the crank won't get into place. The Sram default cups were noticably wider though than the Chris King's. Didn't know that before purchasing.

Here is a picture of this damn thing: http://i.imgur.com/MSfUpHO.jpg
Running a Cinelli Mash.

Cheers!