> I desperately want to get to a point where I'm able to quickly sketch out a statistical model for making a decision, but I'm struggling mightily on where to get started that doesn't include some kind of "hide the uncertainty" shell game, such as how I feel when Bayesianism gets thrown around.

Being comfortable around basic probability distributions is probably the main prerequisite I suggest. If you can understand the uses and analyses of Bernoulli, Binomial, Poisson, and normal RVs, you should be at a point where you can try to model real life phenomena. A surprising amount of life can be modeled as multiple weighted coin flips.