according to the Technical product specification sheet ( http://downloadmirror.intel.com/21958/eng/D33217CK_TechProdSpec04.pdf ) your DC3217BY does only support a maximum resolution of 1920x1200:
See page 23:
126.96.36.199 High Definition Multimedia Interface* (HDMI*)
The maximum supported resolution is 1920 x 1200 (WUXGA).
Connecting a Display which supports higher resolutions than 1920x1200 via HDMI is possible, but you can't display more than the maximum resolution of 1920x1200 on that screen according to the Technical product specification sheet.
Page 25 of the Technical product specification sheet:
1.9.1 Thunderbolt™ Technology Interface
The Thunderbolt controller connects a PC and other devices, transmitting and receiving information for both PCI Express and DisplayPort* protocols.
According to that you might be able to connect a DisplayPort-enabled screen to your NUC, but the maximum resolution of that configuration is not stated in the Technical product specification sheet.
What screen model do you want to connect to your NUC?
Do not have any of those monitors, but I have used the adaptors in the past for dvi/hdmi, I am not sure if dual link displays split the load for 1/2 the pixels on each connection, or switch load between each mhz of refresh. If 1/2 load this might work, if the other and your mini pc does not go above 19x12, not sure what to do.