The reason you are getting that kind of sequencing is because you are trying to use the same wait handle that the producer-consumer queue is using for a different purpose. That is going to cause all kinds of chaos. At some point things will go from bad to worse and the queue will get live-locked eventually.
You really should create a separate WaitHandle to wait for completion of the logging service. Or if the BeginLoggingEvents fits the standard pattern it will return a IAsyncResult that contains a WaitHandle that you can use instead of creating your own.
Have a sequence using a cheap monotonically increasing ID (e.g. With Interlocked.Increment()) so that no matter what order things happen at the client or server, you can regenerate the original ordering later on.
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