Do we have a decision procedure that gives reasonable results for an unbounded utility function?

Not one compatible with a Solomonoff prior. I agree that a utility function alone is not a full description of preferences.

Does the best explanation you have for your preferences that works with a known decision theory have bounded utility?

The best explanation that I have for my preferences does not, AFAICT, work with any known decision theory. However, I know enough of what such a decision theory would look like if it were possible to say that it would not have bounded utility.

I, on the other hand, feel loss when people dither over difficult math problems when the actual issues confronting us have nothing to do with difficult math.

I disagree that I am doing such. Whether or not the math is relevant to the issue is a question of values, not fact. Your estimates of your values do not find the math relevant; my estimates of my values do.