Confusion with mapping a transducer range to a different output voltage range
The datasheet parts you mention show the general accuracy of the sensor, and we can assume that this precision is available in the digital output. The data shown is not affected by the configuration of the analog output.

Alas, you do not show (and possibly you don't even have) resolution and precision specification of the analog output. The conversion from a digital value to the analog voltage is never perfect, and perhaps the resolution or accuracy of this conversion is it a limiting factor in your scenario. If that is indeed the case, you should expect to lose (up to) 50% of the resolution by doubling the pressure range. If the limiting factors lie elsewhere (like in the precision of the sensor itself), changing the analog output configuration does not significantly change the precision and resolution of your application.

To find out whether the DAC is limiting your precision, you do indeed need the detailed specifications of the analog output, just as you imply in your last question.