In my haste, I highlighted the wrong field in the previous images.
The correct field is the Ecliptic longitude. As can be seen, these are
still correctly around 90° on the expected dates for the summer
solstice, but inaccurate for 9 July (even more so). I have retained the observations for midday in all cases, observed from Iraq. They reach exactly 90° by late afternoon on the required days. Note also that the declination (dDec) value reaches 0 on a solstice, and this value is also wrong for the required JW date.
Astronomical almanacs define the solstices as the moments when the Sun passes through the solstitial colure, i.e. the times when the apparent geocentric celestial longitude of the Sun is equal to 90° (June solstice) or 270° (December solstice).
For
reference, I have also included the date for the winter solstice,
showing 270° for the Ecliptic longitude on 27 December 568 BCE and 588
BCE, confirming the correct field is now shown.
Summer solstices:
Wrong JW thing:
Winter solstices: