Bring your system to a crawl??
Showsqueeze is just an "front-end" of sorts for the DivX/WMV encoding engine, so I'm surprised it would crawl your system.
I'd first try setting a "Low" priority to the ShowSqueeze process to see if that helps.
What are these times your system seems to have been hi-jacked by ShowSqueeze? Are you recording something and watching something too (all at the same time)? Are you compressing to UberDVD quality? Is this machine solely for BeyondTV?