While installing Fast Search Server for SharePoint 2010 (FS4SP) on a dev farm today, I got a problem with the provisioning of a new FAST Content SSA (Search Service Application), it would hang forever at "0:01 Configuring the Search Service..." waiting for the TopologyConfigFinish.aspx page to complete.
The problem turned out to be that the SharePoint 2010 Administration service wasn't started after the mandatory server reboot after installing FS4SP. The FAST "nctrl status" cmdlet does not check this. Make sure that both the SP2010 Administration and Timer services are running:
If you still can't create new or delete search service application instances, or make topology changes at all, then you might need to delete the old SSA the hard way. See Deleteing the search service application and How to delete orphan configuration objects from SharePoint farm. Heed this warning: "Please be VERY careful when executing the deleteconfigurationobject command, if this command is not used in the correct way (if you end up deleting the wrong object) there is NO way to revert back the changes and it has the potential to render your Configuration Database useless, hence you may require to restore / rebuild your SharePoint farm".
Remember to configure SSL enabled communication again when recreating the FAST Content SSA, otherwise your next crawl will be stuck on starting while retrying every 60 seconds to connect to the document engine. Also remember to restart the FAST Search for SharePoint and the SharePoint Server Search 14 services before starting a new full crawl.