I have numerous problems with my Search Service Application. Long story short, I want to just start again from a clean slate, but deleting the search service application in Central Administration fails with "Object reference not set to an instance of an object". Trying to delete it with "stsadm -o deleteconfigurationobject" gives the same error message. The application proxy is deleted, though, and it doesn't seem like it can be created again (the list of available service applications when choosing 'Connect' and entering the published address of the SSA is empty).
The source of this problem is that I got the error message "The search service is not able to connect to the machine that hosts the administration component" when attempting to configure search, which I attempted to resolve by changing its connected application pool. When clicking OK in the "Properties" dialog, I get stuck on the "Updating the Properties of Search Service Application". Any attempts at configuring the service application now results in this same endless progress dialog.
So, any good ideas on what's wrong, how to delete the SSA, or alternatively, how to fix it?