I had a similar impression when I took a course on the matter ages ago. I don't have a better cognitive model, but the methods we were shoehorned into with ACT-R were so different from the actual cognitive processes I undertake in completing the same tasks that it all felt so pointless. Short of results derived from massive hyperparameter tuning to overfit existing data, has ACT-R shown any real-world explanatory power?

Yes, very much so. During the last 20 years, a major project has been to predict sequential patterns of brain activation during various tasks based on the activity of ACT-R modules (which have been associated with different brain regions) in models of the task.

All models are wrong, but some are useful. For several decades, ACT-R has been, and continues to be, one of the most useful and influential theories of cognitive architecture devised.

When you say we don't store symbols (in memory slots), would you also disagree that we store symbols at all?

I've never been a fan of symbolic AI. It always felt like the fuzziness of neural nets and pattern matching were a better fit for how we seem to process information, at one level. But it seems like we also perform symbolic logic, typically on demand, possibly as a layer on top of or overlapping the NN foundation.