What video interface are you using from the NUC to the monitor?
HDMI? DisplayPort? DisplayPort altmode of USB-C? Something else?
TL;DR just give us a picture already 
you’ve successfully characterized uncle-Sam. can i get a cookie now ?
The video format is limited only by the capabilities of the monitors and PCs. Both monitors have each two HDMI inputs and one VGA input. The NUC6 has a limitation of only one HDMI and one VGA output. So in each case, the secondary monitor is connected via VGA while the primary monitor is connected via HDMI.
The convergence cradle plugs in to the second HDMI input on one of the two monitors. You can buy a convergence cradle pretty inexpensively on Amazon. The convergence cradle also has a keyboard and mouse input on it, in addition to a single USB-C plug built in to the base. Currently, to use Samsung DEX (an inferior kind of psudo-convergence but you do get a real Desktop), I plug my Note 9 into the USB-C plug. The USB-C is a rigid post that points straight up. So all I do is to push my phone down on to it to connect. The phone automatically finds the large monitor and automatically then goes to to DEX mode (convergence mode) so the keyboard and mouse work then too. Connonical built a full-blown version on Linux that runs under DEX as what appears to be a virtual machine. So when I execute Linux from DEX, I get a full PC-type Linux operating system running on one monitor from my Note 9. Just make sure to get an externally powered convergence cradle. It’ll probably be a wallwart that plugs in to the cradle. Without it, the DEX won’t work and the battery on the phone won’t be able to keep up. Using the wall wart, the phone battery charges while you’re in DEX mode. DEX is only available on a few of the Samsung phones. I am expecting the Librem 5 convergence to work the same way that DEX works (using my existing convergence cradle), given that properly functioning USB-C ports should be the same and because Purism is planning to eventually support convergence.
If your Samsung phone is DEX capable, it will run a Windows-like operating system automatically when plugged in to adequate hardware (no proprietary Samsung cradle is required but you do need an adequately supported cradle). Linux on DEX was a limited beta testing program and is no longer officially available from Conninical (the ISO image) and Play store (the Android app). But six months ago (a year after the trial ended), I found the Linux on DEX ISO image and Android installation file on someone’s website (forget now where I found them). Once you have the image and the Android installation file you can install them and they’ll still work. I haven’t found any kind of limitations to Linux on DEX yet. It uses all of the Samsung hardware resources the same way that it would on a PC. You get a real full-blown Ubuntu linux operating system, including all graphics. Just make sure to only install programs that are compiled to run under ARM architecture.
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