Godel's theorem presents a strictly stronger obstacle than Lob's theorem.

Why do you say that? My understanding is that Godel's theorem says that a (sufficiently powerful) logical system has true statements it can't prove, but these statements are excessively complicated and probably not important. Is there some way you envision an AGI being limited in its capacity to achieve its goals by Godel's theorem, as we envision Lob's theorem blocking an AGI from trusting its future self to make effective decisions? (Besides where the goals are tailored to be blocked by the theorem: "Prove all true statements in my formal system")

Finally, I think it's worth pointing out an actual example of a program analysis tool since I think they are more powerful than you have in mind. The following slides are a good example of such a tool.

As near as I can tell, this is more powerful than other static analysis tools that I have seen (though maybe not, the Google Web Toolkit optimizer is pretty impressive), but it is well within what I expect to be possible, and doesn't get around Lob's theorem. (I can't be too confident in this assessment of its power because I don't see a clear claim of what sort of statements it can prove or how it works except that it seems to detect when inputs to a statement may have invalid values and that it uses brute force techniques to analyze functions and then associates a summary of the analysis with that function (constraints on valid inputs and guarantees on outputs?) so that its analysis of call sites can use the summary.) (This sort of program analyzer is interesting in its own right, and I would like to see a more complete explanation of it, but I don't think it's existence says anything about the problems posed by Lob's theorem.)