In that case, it sounds like EmailProvider = Nonemay be what you want! Have you used that already? It prints the administrative messages to log rather than emailing.
Yes! I remembered this and is part of why I asked That is actually on our short list of things we aim to improve in the next few months, so hopefully we will have some nice features coming your way there! This is a great example with respect to the keys associated with logs, though, so I will make a note to be sure we test this use case!
Have you seen this post about a log forwarder? I thought you might be interested in this Unfortunately, I have been behind on everything and not able to try this out yet