Time in queue

This might get you closer to what you want, perhaps called from OnProcessMessage() in the service:

ClassMethod QueueGetOldest(pQueueName As %String, Output pStatus As %Status) As %String
{
    If ##class(Ens.Queue).GetCount(pQueueName) > 0
    {
        Set tStmt = ##class(%SQL.Statement).%New()                                          
        set qSC = tStmt.%PrepareClassQuery("Ens.Queue","EnumerateItem")
        Set tRS = tStmt.%Execute(pQueueName,"")                        
        Do tRS.%Next()                                                
        Set tHdrid = tRS.%Get("MessageId")
        Set tMsghdr = ##class(Ens.MessageHeader).%OpenId(tHdrid)
        Set pStatus = $$$OK
        Return tMsghdr.TimeCreated
    }
    Set pStatus = $$$ERROR($$$GeneralError,"Not found")
    Return ""
}

It returns the time created of the oldest entry in the queue, or the empty string if the queue is empty or doesn't exist.

You could create a variant that would accept a duration argument and return true/false if the duration between the current time and the time of the oldest entry exceeds that.