Thanks for the response Brett, and for testing this. First the answers to your questions, and then an observation...
Simple Staff List: 1.14
Team Rosters: 2.0.1
Originally I thought this was a theme issue, and I reached out to the developer. (Info Below), But then we saw that Featured Image was working with all the plugin's but Simple Staff List and the Dev suggested a plugin conflict. De-activating ALL plugins, except these 2, results in the issues described. After further testing on my end I see a few interesting things:
When Team Rosters is active, Simple Staff List in the case has a phantom image in the Set Featured Image browse dialog.
For example: In this case with both active, the Set Feature Dialog in Team Roster looks normal. In SSL, there is an unknown (?) thumbnail. Selecting it shows no info. If I deactivate Team Rosters that goes away.
If I switch to the Twenty Tweleve theme everything works - that would normally lead me back to the theme, BUT the theme's Featured Image does work or the Team rosters plugin would fail too. I am not sure where to look in this odd case. The theme technically works - at least with TR, but it is a combo of TR and the theme causing issues, but the only issue is SSL.
Any ideas? I will reach back to theme devs too.