I would guess, given the behavior you describe, that it's one of the post processing effects that is having trouble applying itself to such a large image. I think the basic render process is capable of rendering at that resolution, but the post effects probably aren't designed to do so. This would include GISD, by the way.
I would also note that at very high resolutions your pixels-to-scene-area ratio is going to be much higher and thus, I think, the GI should be more accurate than at a lower resolution *even with lower settings*. Since you are looking at a potentially massive GI cache (generated at render-time even if not cached to disk), consider using low (e.g. default 2/2) GI detail settings, or perhaps even rendering a GI cache for a lower resolution image and using that on the higher resolution final render.
My final thought is to wonder whether the image load/save libraries we use are actually capable of writing files with e.g. a 60k pixel width. This I don't know. I'll try to test it with a simple scene with no GISD or other post effects. See if I can get it to complete, and then, to save...