The flaw in the notion that sentience would reduce God to something less reliable is based in the notion that all of God would have to be equally sentient or non-sentient. But that is not realistic. There are two ways around it.
1) The theology of C.S. Lewis' Mere Christianity addresses this in his theory of the necessity of the incarnation. God has the necessity to relate perfectly to sentient beings.
To some degree, though not nearly as absolutely as you propose, Lewis agrees that sentience is incompatible with omniscience. Sensation is a variety of learning, and what is to be learned? The inability to truly be changed obviates a lot of possibilities for God.
Yet he must also have those possibilities, to be omnipotent. And have the experience of playing them out first-hand, to be truly omniscient. The experience of many mental states can only be known by living through them. (From a Christian angle, he should also relate immediately to those inferior beings who have them, especially if he is ultimately to be their perfectly fair judge.)
Lewis therefore deduces it was necessary for God to fully incarnate himself at least once as each species of truly independent and moral intelligence (subject to final judgement.) Since temporality is an aspect of the notion of sentience, God would not need to always be sentient, but would only need perfect experience of having been so, and having faced the full range of sensory experiences. (So by Lewis's logic, Jesus needed to have extreme experiences like extended starvation, corporal punishment and a dramatic death, in addition to a lot of very positive experiences like the gratitude of the multitudes he fed, etc.)
(Any Gnostic would then step in and say that God, while incarnated then also needed to experience being evil, or at least considering himself evil, to truly understand the intricacies of guilt. So this may lead many places Lewis does not intend.)
2) A simpler approach is pantheism or some weaker relative like "perfect immanence". Such an approach would immediately imply that while the whole of God is omniscient and thus not sentient, we as parts of him are sentient, and the whole can always access the parts. Then even though the whole of God is omniscient, the fact he has both unity and parts allows for the full range of experiences of incompleteness to be known by the perfect whole (including evil).