Your endpoint looks to be incorrect. You have "DIRECT=OS:" in there twice. Try:
<endpoint address="msmq.formatname:DIRECT=OS:meserver\private$\persistenceservice/log.svc"
binding="msmqIntegrationBinding"
bindingNamespace="http://me.logging/services/2012/11"
contract="Me.Logging.Service.Shared.Service.Contracts.ICatchAll" />