Thanks for the input everyone, I ended up going a more brute force method that seems to be working.
I tagged all of the servers to be searched, then filtered them by SourceName so I only had a working pool of logs that were related to the software application I'm looking at. It's a bit more verbose than I wanted but I'm hoping as I get more data I'll be able to refine it.
tag=Backup SourceName="Backup Exec" | eval Outcome=case(EventCode==57755 OR EventCode==34112, "Success", EventCode==34113 OR EventCode==34114, "Failure", NOT EventCode==57755 OR EventCode==34112 OR EventCode==34113 OR EventCode==34114, "Missed Jobs") | stats count by host, Outcome | rename host as "Server Name"
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