I tried to use the PowerShell sample https://docs.microsoft.com/en-us/azure/azure-monitor/platform/data-collector-api#powershell-sample without any changes.
It completes with status 200 (OK) and correctly creates a new table with LogType (MyRecordType) within the Custom Logs in the portal (Log Analytics Workspace->Logs).
However, the events that are submitted don't turn up there - there are always "No results from the last 24 hours". Also, within the new table, none of the custom properties are created.
Has anybody observed a similar problem? (Some people seem to be using the C# code successfully.) Thanks!