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Diffuse transmission through small and crowded geometrical structures is one of the fundamental weaknesses of a backwards raytracer. You would need to massively crank up -ad, -as, and probably a few other parameters to see more light coming through those narrow and deep gaps in your model. The results might still not really be satisfactory, though.
This methodical difficulty is the reason why the genBSDF program was created, which I assume is the tool behind what you call "OpenStudio Blinds BSDF". So it's no surprise that you're getting more reasonable results that way.
The "internal inconsistency" is easy to explain once you recognize the problem with the narrow and deep gaps. The two scenarios would probably converge a lot better (ie. at similarly bad values) if you were to add another slat at the top of the windows. Right now, both models have a comparatively unobstructed zone there, where daylight will reach the ceiling after a single diffuse bounce off the top slat. Just that in one case, that zone is three times as large as in the other.