Intel has posted the following document that might be able to help you: Intel® NUC Boards and Kits — Remote Access to Intel® NUCs
Try BIOS update: Intel® Download Center
Latest graphics driver: Intel® Download Center
Loading the latest drivers was done upon installing W7 and that had no effect. Updating the BIOS was done after the problem started and that also had no effect.
Read the article you linked to and it's definitely similar in nature to my issue here but that solution there did not help. I might try the 2X RDP Client though.
Ultimately I changed the settings on RDC to turn off "Desktop Composition" and "Persistent bitmap caching" both of which appear to need to be turned off for the black screen issue to stop. Why those matter I don't know. Never ever touched those in years of RDC connections. Something to do with the Iris graphics?
I see one of the suggestions at the link was to remove the Intel graphics driver and instead use the generic Microsoft one but that seems ridiculous to me since one of the selling points of the NUC is the Intel graphics!
So, I'll run this way for a while and see how it goes.
Thank you for the reply.