Another possible explanation for the MS Pro drying up more quickly during low angle sun in the morning (and therefore warming faster) is simply an insufficient protection from solar radiation, heating and drying the sensor chamber more significantly than other shields and therefore seeing faster warming. That would in fact be a negative for the MS Pro, whereas the theory about better airfow would obviously be a positive. Very difficult to judge.
The last part of your message contains the great truth of this fascinating subject.
From whatever angle we observe these differences, we can only hypothesize the reasons, the lack of knowledge of the real measurand imposes humility and respect.
It is true that there are many reported episodes that suggest a problem with the Barani in the management of low-angle lateral sun radiation, and low angle does not mean low intensity, this aspect is real and there are many reports on the matter that would suggest it is real
The discussion regarding overcooling is much, much more difficult, here we are no longer talking about management of incident or reflected radiation, and it becomes extremely difficult to make an assessment with the modest means at our disposal.
Certainly, the Barani is, fundamentally, an "open" screen, this puts it in a position to make the most of natural ventilation, if present, but it also puts it in difficulty in other conditions
M.