I often have to join meetings using other meeting products so I am somewhat familiar with common features. Of course, GoToMeeting is my strong preference because of the rectangle sharing feature which makes it easy to switch between the many windows I share on my large, 4k screen. I often have to show Word requirements docs, Mockups, PDFs and various browser tabs which I drag into the rectangle.
You already have my +1 to remember the last rectangle size/location.
My suggestion is this:
Rather than me drag apps into the rectangle, I could place them around the each of my main screens.
1. Every time I share a window, add a side "tab" to your control panel to represent that window.
2. When I want to go back to a previously shared window, I just click the small tab that was created the first time that window was shared.
3. I suggest to show the app's icon in the tab and hovering would show the window title so I know I'm about to switch to the correct instance of PDF or Word etc.
Now I can see all windows AND quickly switch between the ones I am using in this meeting.
I may even pre-load these windows/tabs before attendees join the meeting.
Future - you can grow into this over time if proven popular:
1. Pre-define my favorites and make the available tabs as default meeting setting. If the referenced app is not running then disable that tab until it is running. (Or double-click or ctrl-click would launch that app)
2. Eventually have meeting profiles of defined tab groups for different types of meetings to share different types of windows.