When I programmed Pascal decades ago, I had my own lib, which was huge, it was just a massive collection of functions pulled from projects which I all wrote myself and all remembered (and still remember). When I had to build something, it was mostly cobbling together those functions. Worked a lot faster (with more stable results) than Google->SO or npm search and install.
APL(/j/k) have that but with the added benefit that you don’t have to write or download a library; everything is composable, so instead of remembering/searching the functions I (or someone else wrote) remember the actual implementation... Which, in those languages, is usually the same amount of chars as the function name and usually smaller than the function name with params.
It's the same thing as when you learn various other languages and you start to not appreciate how to appropriately model data in that language, which leads to excessively complex or inadequate types.
IMO, the elegance of a notation is not defined by its ability to prevent people from writing bad expressions, but by the capacity for good expressions to be practically and usefully leveraged. A good notation is about empowerment and clarity, rather than about prevention.
Approaching it sort of like you would a small Lisp isn't ideal/is a flawed approach but may get you closer: acknowledging it as a separate, distinct paradigm is pretty much necessary to get a feel for it. I think the easiest way to bridge the gap right now is probably learning a concatenative language, just because the resources for teaching those are so far ahead of what APL has right now (the best way I can think of to learn to use notation effectively is by reading one of Iverson's books that use J as notation or doing one of Iverson's J labs) yet still give you a feel for where the paradigm is headed.
Summary: give J's labs a try, they might help you get a hang of the paradigm better; KEI was a fantastic teacher, and Chris Burke, Roger Hui and Eric Iverson have done a great job in maintaining the old & making new labs, and if that doesn't work, try learning a concatenative language first and carrying it over.
My stumblings in APL involve a continuous adjustment of functions and data to fit each other, an impedance matching, a continuous going up and down lochs, now to enclose this, now to align this vector with that nested vector, now to mix that nested vector into a matrix to feed into a function with a first axis rank adjustment.. and it feels like a system built of ill-fitting parts because of it.
Perhaps it’s not APL inherently being an elegant notation, but smart people’s ability to express their thoughts elegantly in whatever notation they are using?