I cant follow the idea, normally its done like this:
Calibrators like the Fluke 5440 or 57XX-series use a PWM-DAC and two zener-refs in series (2x ~7V =14V), which gives them the ability to go from 0 to +-11V.
Using a trimmed 10V-reference for the DAC isnt necessary, since all calibration constants are used in software and the needed internal zener -> 10V-converter would worsen the overall specs since it contributes additional long-term-drift, TC, noise.
Your calibration procedure looks very similar to the Fluke 752A which is usually used for this type of calibration (when left-side voltage reference + DAC is seen as a calibrator).