Thesis 1: The problem of divine hiddenness is, in some reasonable sense, a “deeper” problem than the problem of evil.
Datum 1: If God were vividly present to us, we could suffer almost anything–at least the kinds of things we find on this planet–without (evidential) doubt that God exists (and also with little emotional doubt).
Caveat 1: Datum 1 notwithstanding, one clearly could have some (evidential) doubt that God existed, even if God were vividly present to them throughout the suffering. For one could have a good argument that one were hallucinating whatever experience it was in virtue of which God was present to them. In fact, if one’s prior credences were distributed in certain ways, they coud be nearly certain that they were hallucinating. It is an interesting question whether any reasonable, properly functioning individual could have such credences. I doubt that it could be so in any nearby world. (Emotional doubt (or “psychological” doubt, it you prefer) is often irrational, so it can arise under any circumstances.)
St. Stephen, Protomartyr: So my thesis, taken generically, doesn’t face a serious problem from the Proviso. My focus is on situations pretty similar to the actual world. A core example is that of Stephen. In the Scriptures (Acts 7:54-8:2), as Stephen is being stoned to death (quite unjustly as part of a terrible persecution in which Saul “dragged off men and women and committed them to prison” (8:4)), he says he see’s Jesus, then a bit later he asks Jesus to receive his spirit in a standard formula of acknowledging imminent death, then finally prays for their forgiveness.
The implication seems clear that the way he accepted his death is importantly related to (inspired and sustained by) his experience of Jesus being present to him (in some kind of vision, in this case). There are other similar stories both of historical martyrs and one’s I’ve heard more closely. Contrast this “peace that passes understanding” with cases where people feel “alone” during suffering and have a kind of irreligious experience (See Gellman 1992 and my enormous MS on the “Common Sense Problem of Evil) that serves as data for an argument for atheism from evil.
Caveat 2: I think that, formally speaking, the problem of divine hiddenness *just is* an instance of the problem of evil (my Routledge Encyclopedia entry on Divine Hiddenness discusses this (it’s behind a pay-wall, sorry but I’ll send it to you if you want). In light of this, I have to modify my thesis slightly (but not substantively).
Revised thesis: The “real” problem of evil *just is* the problem of divine hiddenness.
Action point: For my own part, I will be focusing much more on the reasons God hides (in the sense in which he does, I mean, almost everyone believes in God or at least the supernatural, so there’s actually a problem formulating the problem, which I also plan to work on) than on the reasons why he allows evil in general (confession: how did that ever get to be a “problem”?). I will continue to spend time on special cases like animal suffering (more to say there than appears in _The Problem of Animal Pain: A Theodicy for All Creatures Great and Small_, I cut three chapters and have had many thoughts sense. But I think of the following two questions
Q1: Why would God allow S to suffer *that*, X [insert horrendous evil]?
Q2: Why wouldn’t God be a present comfort to S as she goes through X?
we have more to learn by pursuing Q2 than by Q1. (Call that Thesis 2.)