After speaking some more with the client, they mentioned that they had run the BizTalk Message Box clean-up stored procedure (knowing it was unsupported in production) more than once in the past year, and the problem was getting worse in the last couple of months. I then started digging a bit deeper into exactly how the tracking data gets moved from the BizTalkMsgBoxDb to the BizTalkDTADb and found that there is a table in the BizTalkDTADb that keeps track of the last Sequence Number moved from the BizTalkMsgBoxDb tracking_1_X table to the BizTalkDTADb. I then looked at the current number in this table (TDDS_StreamStatus) and they were not even close to the Sequence Numbers in the trackingdata_1_X table in the BizTalkMsgBoxDb.
After fixing this Sequence Number mismatch the tracking data started to move as expected and over the next hour or so the CPU usage on the BizTalk SQL server dropped significantly low and back to what I would have expected on a BizTalk system with this amount of load.
The tools that can be used to fix these sort of issues it the BTSTerminator and it can be found along with other BizTalk Tools here: http://msdn.microsoft.com/en-us/biztalk/dd920317.aspx