Symmetry between up and down quarks is more broken than expected

It's not as bad as that. AIUI, the essence is, if you've ever seen the concept of a Feynman diagram and summing over all possible interactions, that works well for electromagnetism and some other interactions because the alternative terms fall off very quickly. For the strong interaction, they fall off so slowly that it takes massive amounts of computing power to walk through all the alternatives, essentially infeasible amounts of it. So we have to use some heuristics. If it turns out one of our heuristics was wrong, well, that's actually happened a number of times before.

So it's not quite as bad as "you just hit the model until it says what you want it to say". It's more "your shortcut broke so take less of a shortcut and you may discover that the standard model worked better all along than your shortcut". Which, again, has already happened multiple times.

In fact it is quite frustrating to physicists that the standard model always wins these fights. They'd love for it to break in some concrete manner, which is why they're always going on about this break or that break. As it stands now, in some sense, every time the standard model is vindicated it's a worst-case scenario for particle physics. It's not like there's a cartel trying to defend it... everyone would love to be the one who definitively broke it! It's virtually a guaranteed Nobel prize.

Can’t you just run the heuristic over many many runs to build up a probability model? i.e given we simulated a trillion times while varying inputs and we got marginal error, we’re 99.99999% certain that this function follows what we observe 100% of the time etc?