I agree with the hint at a timing cue but still don't think HAL 'went insane', I more agree that he found an 'insane' "solution" to a problem humans would find

I agree with the hint at a timing cue but still don't think HAL 'went insane', I more agree that he found an 'insane' "solution" to a problem humans would find intractable. The "just a moment..." can be thought of more as an auditory interface representation of "processing", where HAL is exploring the solution space of ever more unlikely solutions until it has at last resolved a statistically superior solution.