In this case, yes I think your expectations are a little high.
What you are trying to do is produce an accurate scene referred color in a print, but you are missing a step, because you haven't determined exactly what that color is.
For this, you need to measure the color of the paint on your exterior wall with a spectrophotometer and then process the file to reproduce that in print as close as possible.
Without the external reference, you are hoping that the sensor response and raw conversion produce an accurate color, which is then printed as it appears on screen. That is not likely (as you've found out) to be the case.
To produce an accurate scene referred color, you need to process to specifically produce that color. But without a reference of what that color is, the best you can do is trial and error until you obtain a print that is a close match.
We are relatively good at seeing hue differences in two references held up side by side, so by holding the print up against your paint, even slight differences will be visible.
The easiest way you'll produce a close (but still not exact) match will be to take a paint scraping to the paint supplier and have them measure it with a spectrophotometer. They'll then be able to produce something close.