Where did the supine form originate? It seems strange that for there to be a verbal noun with only accusative and ablative forms. This, at least to me, suggests that there was once other forms, especially as the supine can often be replaced with other grammatical structures. Is the supine some sort of hold over from old Latin, or some other language, and if so what was it used to convey?
The supine indeed appears to be the relic of a verbal noun. You can derive fourth declension nouns from the perfect participle stem, and the meaning is similar to the third declension derivative in -io: e.g. movere > mot- > motus & motio.
This fourth declension noun (e.g. motus) was used flexibly as a noun. Plautine Latin shows far more flexibility than classical authors. By the classical era it seems that all forms but the accusative and ablative (and maybe a rare dative) had fallen out of use. Since most forms were lost, it no longer behaved as a noun.