It's somewhat less constructive than reinventing the wheel, actually. It's axiomatic, not empirical.

If A2-A1 > B2-B1, and A1 = B1, then A2 + B1 > A1 + B2 is about as insightful as 4+2 > 2+3, or 2n +2 > 2n +1. Once you set your definitions, the meaning of ">" does pretty much all your work for you.

As I understand it, your goal is to derive some way of assigning utilities to different outcomes such that they maintain preference ranking. I believe this could be done about as well with:

"Assume all outcomes can be mapped to discrete util values, and all utils are measured on the same scale."

This gives you all of the properties you've described and argued for in the last several posts, I believe, and it takes rather less effort. I believe you've assumed this implictly, though you haven't actually admitted as much. Your system follows from that statement if it is true. If it's false, your system cannot stand. It's also rather easier to understand than these long chains of reasoning to cross very small gaps.