I agree with the virtualization suggestion. While I was creating a VM today, I happened to look in this section of the settings in the VirtualBox manager application:
It's a feature I've never used, so I can't speak from personal experience, but when I saw the Allow Multiple Connections setting, I thought of your query.
Perhaps you could run the desktop you want to share on a VM, and allow multiple connections to the display? Sorry if it turns out to be a waste of time, but I thought perhaps it might help you.
ALSO: You might want to consider using Whereby, the meeting software. Many of my family members are at remote locations, and we use it every two weeks to have a family chat. Rather than type a lot about it here, you can find out all about it at whereby.com. I've noticed during such a family chat that there's a "share desktop" function available. We've never needed to use that, but it might be just what you need.
Did I mention that it's free, for meetings up to 100 participants for 45 minutes at a time?