Yep. I agree 100% with John's rabbit hole statement.
Late 2013 supports 4K, but not at 60Hz .... only supports crummy 30Hz or 24Hz. And it should support 2560x1440 @ 60Hz via the mini display port.
I have the same model Mac as the one referenced in John's original question. My external display is the last Cinema Display model that Apple was selling before the first Thunderbolt Display came out. I have had some issues trying to drive that display, but they come and go. I am tempted to get a genuine Thunderbolt Display, with the hope that that will make a difference, but maybe I should try a non-Apple monitor, just as John chose to do.
Thanks!