That there is an immaterial realm of ideal forms (structures, concepts) of which our universe consists solely of imperfect approximations of.

This stuff about imperfect approximations is just a remnant of Plato's mysticism. Few modern platonists would say anything like that. This notion of an immaterial "realm" has similar connotations. How about:

Platonism is the view that there exist such things as abstract objects — where an abstract object is an object that does not exist in space or time and which is therefore entirely non-physical and non-mental.

Platonism is appealing because it adheres to our norm of accepting the existence of things we make true statements about. "Silas is cool" implies the existence of Silas. Similarly, "3 is prime" implies the existence of 3. The list of non-platonist options as far as I can recall consists of: mathematical objects are mental objects, mathematical objects are physical objects, statements about mathematical objects are false (like statements about Santa Claus), or statements about mathematical objects are actually paraphrases of sentences that don't commit us to the existence of abstract objects.

It seems like you are trying something like the last. But for this strategy you really should give explicit paraphrases or, ideally, a method for paraphrasing all mathematical truths.

I would say instead that there is some generating function for reality. A system of inscriptions/rules can describe that generating function imperfectly; but this in no way means that the rule/inscription system has some existence apart from its instantiation as the universe itself, and again explicitly in a model.

But then what kind of thing is this function? It clearly isn't merely a set of inscriptions and rules for manipulating them (the models). Nor is it merely the physical universe. We talk like it exists. If it doesn't, why do we talk like this and what do claims about it really mean?