I think the non-intuitive nature of the A choice is because we naturally think of utilons as "things". For any valuable thing (money, moments of pleasure, whatever) anybody who is minimally risk adverse would choose B. But utllons are not things, they are abstractions defined by one's preferences. So that A is the rational choice is a tautology, in the standard versions of utility theory.

It may help to think it the other way around, starting from the actual preference. You would choose a 99.9% chance of losing ten cents and 0.1% chance of winning 10000 dollars over winning one cent with certainty, right? So then perhaps, as long as we don't think of other bets and outcomes, we can map winning 1 cent to +1 utilon, losing 10 cents to -100 utilons and winning 10000 dollars to +10000 utilons. Then we can refine and extend the "outcomes <=> utilons" map by considering your actual preferences under more and more bets. As long as your preferences are self-consistent in the sense of the VNM axioms, then there will a mapping that can be constructed.

ETA: of course, it is possible that your preferences are not self-consistent. The Allais paradox is an example where many people's intuitive preferences are not self-consistent in the VNM sense. But constructing such a case is more complicated that just considering risk-aversion on a single bet.