What an interesting discussion! I've pondered a lot about the concept of guilt, as well as shame, just for my own self, and it's really reassuring to see that even those who seriously study these phenomena agree on the "lack of conceptual clarity...Measures of guilt do not correspond well to the definitions from which they derive".
Illustrating both feelings in simple common phrases, I would say guilt is the "Look what you've done!" admonishment, while shame is more like "What would the neighbors think?" In both cases it's an indirect way to put the individual in charge of their own punishment, a convenient way to educate them into the norms of society (if they are children) and manipulate them into compliance (in case of adults). Whether there's a difference between the two may be debatable.
Coming from a European background (I was baptized catholic too, but thanks to plenty of atheism / agnosticism in the last generations of my family, religion had little impact on my upbringing) I am very familiar with guilt. The same thing can't be said about so much shame, which seems to recall some stuffy, archaic notions held in high vregard by the petty bourgeoisie in the past centuries, and appears completely outdated in today's culture. At least in Europe! In East Asian cultures, on the other hand, it appears to me that shame is a much common tool to make people toe the line. (Not sure if the experts agree on this.)
It's quite interesting how you highlight the relationship between guilt and depression, eating disorders, and OCD that it can cause. I interpret this as an invitation for all of us to overcome our own guilt, and help each other do the same. I think it's so much easier to stop feeling bad about ourselves if the people around us show us that we don't have to beat ourselves up. I would even go as far as saying, it is an important process for a better functioning society.
What I have seen in people who overcame guilt is a heightened sense of moral and values, as they became more conscious of the things they refuse to feel bad about, while consciously making sure they don't fall off the other side of the horse into arrogance. "Yes, I know exactly what I've done. That's why I'm the one who needs to deal with it."
Those people who have overcome their feelings of shame... they tend to shine in a radiating light of exciting beauty and confidence. "The neighbors are free to think whatever they want. It's their business, and none of mine."