OK, I figured it out.
Below is a picture of the connections I made to connect the 16.000000MHz TCXO.
But here is the BIG news...with the power off, press and hold the SET button while powering on the MHS-5200A. WALA! A calibration menu appears. I haven't had time to write up the details, but for me a 5000 frequency number gives the best result, although I don't think the ratio is able to directly work with 16.0000000MHz, so you may want to bend your reference a little to get exactly on. Of course, I am into measuring frequency within .1Hz at 20MHz, so you may not need to be that exact. Maybe someone else can play around and help me out. There is also voltage level settings in the calibration menu.
Bad news for the frequency counter...displays 10.000074 on the self test when fed with the 10.0000000, regardless of cal setting, but that's still really useful. I think that's in the coding, and it is consistent (1.000007MHz for 1.000000MHz in).
If you hold the top left button (CH1/2) while powering on I think it factory resets.
Just get a 3.3V 16.000000MHz TCXO and connect the 3 leads as show below. I don't have a picture of the "after" with me here at work. Once I was able to "un-calibrate" the factory error correction I have a dandy little agile generator, and it has great resolution and accuracy in the area below 1 MHz! It stays within 1 Hz at 10MHz through a range of room temperatures. I use it to verify my GPSDO and other references aren't wobbling, and also to drive other radios reference crystals.