I apologize to all for my poor forum etiquette. I thought my problem was T-SQL related. I was wrong, and my query's poor performance seems to have a DB issue.

...I put CPAS into single-user mode to lock out users. I've put it back in multi-user mode and rerun the backup. It's running now.

...Even though CPAS could not back up, the error file does seem to show problems with indexes. How do I rebuild all the indexes?

...The backup job just finished normally, and the "long-running query" ran in 4 seconds. Back to normal.

...My backup job does reorganize the indexes, so maybe that fixed it. I dunno.

I really appreciate everyone's time and attention. Again, I apologize for the "dual-threaded" post. It was not meant to be that way.