You may be interested to hear -- if you haven't already -- that this idea led to a new site feature:
Talking Tolkien, a soon growing collection of analysis of 'Tolkien-words'.
I have never heard of any Polish influence to Tolkien. I only know his statement "I can't write Russian and find Polish rather sticky yet" (Letters).
Syntagmatic is a high-brow term with a low-brow meaning, it basically just means 'in the context of a sentence', as opposed to the also mentioned
paradigmatic, where words that could have been used instead of the word in question could have been used. Paradigmatic observation basically just means giving synonyms, or definitions.