Greek Phrase Word Order that Miscommunicates

Point well taken about being careful about the phrase order. You have two grammatical errors in your presentation. προσεφερον is not a participle, contrary to what you said. Also, the prepositional phrase "to him" is in there. The preposition is προς (to/toward), prefixing the above verb as a compound. Koine Greek is what linguists would describe as a "fusional" "synthetic" language, which very often combines morphemes, "synthesizing" words by "fusing" the morphemes together. It is important not to overlook the often arbitrary word compounds in the language.