And the point is that it's not about modeling!

What happens is that we invent crazy math that is not supposed to have applicability, then some years go by and it's like, oh my God, quantum mechanics is somehow exactly all about the operation of unit Hermitian matrices... how crazy is that?? etc.

If it were some kind of model that we are able to successively refine, the progress of discovery would look something like a Taylor series, and it would be no surprise that we are eventually able to model phenomena within some tolerance epsilon.

But that is not what is happening! Rather, it's that we discover that some large and sophisticated piece of math, for which we had not thought of any particular applicability, turns out to exactly represent specific advanced physical phenomena. This happens over and over.

I'm confused by your statement that "Math's not the only modeling medium that can be Unreasonably Effective", because it's not clear to me what the notion of a "non-mathematical model" means. (That is to say, it's not clear to me that you're even correct in the weaker assertion that "Math's not the only modeling medium.") Can you explain?

Modeling media besides math: digital electronic circuits, analog electronic circuits, legos, quantum mechanical phenomena, gears, computer simulation, wetware, mythology, clocks, BZ reactions, ...

Several of those are, in fact, math. (In particular, computer simulation.) The others are mostly phsyical models, which I must admit, I had not thought of. So that yields two; mathematical models (that is to say, formal models) and physical models (that is to say, real-world models). (The line can perhaps be a bit blurry in the case of e.g. digital electronic circuits, but, well, I'm not claiming there's a sharp line.)

That leaves "mythology", which I'm not convinced is a proper modeling medium at all.

But those are examples of modeling math, with a superficial layer of physical material. Another way to say it is the degree that these are useful models, is the same degree to which they reflect mathematics. With the possible exception of mythology.

Many of which are reducible to math. Though I'm not sure what legos have been "unreasonably effective" at predicting.

Did you read the essay? Actually, both of them? The reason mathematics is considered Unreasonably Effective is because we have never seen anything with similar effectiveness. Ever.