Sorry to post on an older thread, but it is still a relevant topic.
I was hoping to maybe explain the situation in a different way and see if hopefully mediashout is working on a solution. While I understand mediashout may be focusing on live presentation to an audience, so are your competitors. They've also been innovating to definitely meet the needs of this new "normal".
When we had to move to streaming, something we had not done prior to 2020 the easiest solution was to capture the second monitor (our projector) for the broadcasting software, in order to overlay lyrics during worship. As we progressed we found it much nicer to make the text with a transparent background. This caused us to forgo our nice looking slide background for a solid color so that we could chroma key it out (like a green screen effect). This made our slides which project locally look meh (as they are on a black background), but at the time we did not care as nobody is in service.
Now that we are looking to allow in person worship, along with streaming, it would be nice to have both a clean slide for the stream, and also be able to have our nice background for those in person. However the only way to do that currently would be to plug in another monitor to use as a stage display. With other software such as propresenter, it's possible to set this third display as an NDI output, so it is virtual. That way we can achieve the same goal without having to plug in a third display that I'm just going to hide under the bench or something.
Hope this makes sense. I really hope this is a feature that may be on the near term feature list. We've been using mediashout for over a decade and I'd rather not have to switch and learn new software.