Neat, but this looks equivalent to Harsanyi to me. It seems to me like you make the same assumption that VNM holds for the subvalues; your are the equivalent of the agents being aggregated in Harsanyi's society. If you're inconsistent about "your welfare," then you can't aggregate that and your other subvalues into a consistent function.

Now, if someone makes that objection- "but I can't compress my welfare down to a mapping onto the reals!"- you can repeat this argument to them. Well, can you compress subsets of your welfare down to a mapping onto the reals? And if you can do that for all of the subsets, then we have a set of mappings onto the reals, which we can aggregate into a single mapping, and you were mistaken about your preference inconsistency. (Now, they might be unsure about the weights for those mappings, and there's no guarantee that you can help them pick the correct ones, but that's a measurement problem.)

I suspect this may be a more convincing argument that people should be optimizers: if the feeling of cyclical preferences is the result of uncertainty, then that uncertainty might be resolvable, whereas Dutch book arguments just argue that their preferences are a bad idea, which humans often find unconvincing. Indeed, whenever I've seen someone defend cyclical preferences, it's by altering the saliency of various variables for the various comparisons, and it seems easy to point out to them that they're not making a nuanced decision, but just making the decision based on the most salient factor, and that if they carefully measured their preferences along all relevant axes, they would know which option was the best, all things considered.