Your take on the modal argument is quite superficial.

Intentionally.

The argument works if we begin from the existence of any particular contingent thing.

And the conclusion is the same: anything can be placed on the last item. Note that I made two criticisms: declaring the universe to be contingent and adding external requirements ("hidden premisses") to the argument.

The conclusion of cosmological/modal argument is that something must exist by itself (not created), but the argument by itself doesn't add any requirement on the nature of this thing (and mixing it with others arguments as if was an unity is what I call dishonesty and "confound the reader")

On Plantinga: once I debated using this definition of his argument. The article itself notes that (7) is the weak point. The reason is that (7) is an affirmation instead of a logical conclusion. If we admit that (7) may be false we have the following: (7) It is not the case that God necessarily exist. (8) Therefore: God doesn't have necessary existence. (9) If God doesn't have necessary existence, then God doesn't exists. (10) Therefore: God doesn't exists.

Others version may have a similar flaw, i.e. using an assertion instead of logic development.