Macbook Pro CH340 Nano 14201 error
Timekeeping isn't exact with any of the boards, though .05% - just over 7 minutes/day - doesn't sound like too high an expectation. 

Restarting when you connect it to your computer is by design and doesn't indicate a fault. Opening the IDE's terminal or connecting another terminal program to a connected and running Arduino will - and is supposed to - reset it. Here is a forum discussion on how to disable the auto-reset function (Uno-specific) if you want to. Note that it involves modifying the board.

It's quite possible that this one board has a fault, though it still could be the cable. A couple of swaps should confirm it one way or the other.

I'm still not clear on where the error message, 


  ser_open(): can't open device "/dev/cu.usbmodem14201"


came from, but I'm guess it's from AVRdude, the uploader application on your Mac, and still I'm wondering if the correct port is selected in the IDE's Tools | Port menu? For some reason, a USB device called "cu.usbmodem14201" is expected but not found. Since neither the Mac nor the IDE inherently knows this name - a USB device announces its name when you connect it - could this selection be left over from having previously used the genuine Arduino? Another reason to check the Ports menu. Also note that the Ports menu doesn't update its list spontaneously - only when you open it (and maybe only when you open the top-level, Tools, menu; I don't remember exactly).

Update:


  The regular Arduino at 0.5% is pretty crude, I'd pay more for a more
  accurate crystal, but I was able to develop a sketch that adjusts for
  the Arduino's inaccuracy.


You could try putting the Arduino in an "oven" - and I emphasize the quotes. This is not a heating chamber per-se but a temperature controlled chamber. If you're getting good results by adjusting the count, adding the oven should get you even better results, especially as the seasons change and if that makes enough difference where you are.