When using the external reference, when using the internal reference, I think that the way internal buffers are different.
Please show us the arrangement of the buffer at this time.
I want a block diagram.
I was shown in the following thread that the input impedance varies depending on the selected gain.
In the data sheet, the structure of resistance strings is posted next to the figure you show.
I would like to see a mechanism by which the input impedance changes, depending on the gain chosen.
Sorry to trouble you.
I thank you in advance.
I was hoping for a buffer between the Resistor String and the reference terminal.
I assume that the Resistor String and reference terminal are as direct as you say.
At that time, when connecting a resistor in series with the reference terminal, a current flows from the reference terminal to the Resistor String, so that resistance seems to influence the accuracy.
Is not there another buffer somewhere?
the way you are dealing with this problem is not optimum, as the 1kohm resistor in series acts as a resistor divider with the internal string DAC, which in addition degrades all the specs, like drift, or gain error.
You can do couple of things,
1- add a JFET switch or similar and connect the external reference one the internal has been disable.
2- Disable the internal reference after power-up the device. During the power-up will be a short circuit but it should not be higher than few mA so, I do not believe is going to be destructive.
3- use a different DAC without internal reference.
Note- the DAC should be powered at least to the same voltage than the external reference.
Note II- why you are not using the internal reference and Gain = 2 to get a 5V output?