Let the doctrine of absolute divine aseity be that God is responsible for all truths --that all truths depend on His will--even truths like, "2 + 2 = 4." By extension, this would mean that He is responsible for, "Necessarily, 2 + 2 = 4," "Necessarily, two negatives are a positive," and so on.
But this would then mean also that God causes, "Necessarily, if something is necessary, it is actual," to be true. That is, the DADA would imply that God is responsible for the truths of modality itself just as much as any other truths. But this is self-contradictory, i.e. it is a contradictory description of modality. Therefore, the logical truths of modality do not depend on God's will, and so God is not absolutely a se. (He is a se otherwise conceived of, but not in this sense.)
I follow Avicenna's idea that truth is in the essence of things, which I think sidesteps the problem you raise. Assuming God designed the universe originally as 'very good' (or perfectly true; i.e., perfect), truth in the essence of things would naturally create the dispositions, tendencies, natural progressions, etc. of creation as it unfolds. From this, I assume also that the story of the fall (whether literal or allegorical is unimportant) reveals that man's will via wrong choice injects falsity into an otherwise true universe which affects changes not in substance but in
quality of both essence and matter. This qualitative 'stain' spreads causally into creation creating instances of imperfections of all sorts, in matter (disease), spirit (corrupting the animating force) and mind (mental defects).
Another way to look at it is that it isn't God's will that demands 2+2=4, it is the effectual nature of truth in the essence of things which steers our perception the propositional and all intellectual operation toward true answers. It's in His design, not in some whip in His hand.
The point is that in this view, God's "will" can be largely removed from where truths or untruths land in His creation. His desire is for a perfect universe which shares with Him the most fundamental building block of His essence and all existence--truth--but this is currently tarnished by the effects of a fragmentally falsified existence which naturally produces all those tendencies associated with truth falsified; doubt, defective reason, ambiguity, shortcomings, afflictions, diseases, uncertainties, etc.
It's the Christian's hope that He's bringing everything to His desired end.
This view may seem to place God outside His universe re the wound watch theory, but I hold that He works diligently and continually within the lives of all in creation to stop us short of our own destruction and produce forward movement toward the true/good in culture, education, science, etc.
Maybe the pathogen of falsity has to run its course before creation can be properly and fully healed [restored to its true state].