Thank you for the excellent suggestions.
I did confirm that my time range was not a limiting factor (searches were for 'All Time') and we had previously cycled the syslog process locally via 'esxcli system syslog reload'.
I tried your search phrase suggestions and the latter returned hits unfortunately they were for three separate (different) hosts than for the one we know with surety was PSOD-ing.
From a timing perspective we did add Log Insight as a syslog target after the PSOD occurred so perhaps this is a limiting factor (although we confirmed that the Host is sending some of its logs as evidenced by Host name queries it seems like not all of the logs were sent).
Would it be expected behavior to drop this particular vobd.log on any ESX host that is configured with Log Insight and have that log be searchable (is there any value in sending you our specific log to test this scenario)?