The pasuk in question is:
וַיִּכְתֹּ֨ב מֹשֶׁ֜ה אֶת־מוֹצָֽאֵיהֶ֛ם לְמַסְעֵיהֶ֖ם עַל־פִּ֣י יְהוָ֑ה וְאֵ֥לֶּה מַסְעֵיהֶ֖ם לְמוֹצָֽאֵיהֶֽם׃
and as we can see in this trup chart I made, within the first half of the pasuk (marked by etnachta), the first thing marked off it al-pi-Hashem. Thus, "by the word of the LORD" applies to the full phrase, and the verb of that phrase is vayichtov.
Lion Of Zion noted this in a comment on that post, as well as in his own post, "Did Ibn Ezra Follow The Trup?" He notes that Simcha Kogut notes that Ibn Ezra makes several declarations about the importance of not varying from the peshat given by the author of the trup, yet in this instance, and elsewhere, Ibn Ezra diverges!
For more examples of Ibn Ezra diverging from trup, see Shadal's Vikuach Al Chochmat HaKabbalah, and specifically this post.
Whether or not the trup is like him, there is certainly reason to think that Ibn Ezra is correct in his parsing of the pasuk.
In terms of trup, presumably, if in accordance with Ibn Ezra, we should have a zakef on motzaeihem, so that lemaaseihem al pi Hashem goes together. But that would awkwardly separate motzaeihem from lemaasehem and keep it with vaiyichtov Moshe. Perhaps we should separate off vayichtov Moshe first, with its own zakef?
(I would note that this division, as pictured above, accords with Wickes' principle of continuous syntactic dichotomy, in which you take a phrase beginning with a verb -- in this case vayichtov and chop off noun phrases and prepositional phrases from the end. I wonder, then, whether a case could be made for Ibn Ezra, in which the fact that the prepositional phrase at the end, al-pi Hashem should be lopped off first, even though by rights it is part of another prepositional phrase. Especially if they pay heed to syntax in a way that is not extremely deep. I would like to see other examples or counterexamples of this construction before making judgment on this. However, since this is justa nagging idea, I will assume for now that indeed, Ibn Ezra's peshat is against the trup.)
However, the question is whether Ibn Ezra thinks he is against the trup. As Lion of Zion quoted Ibn Ezra:
"There is a general principle that there is no sage like the מפסיק [the one who divided up the text with trop], for we have seen that in all of Scripture he did not place a disjunctive accent except for where it belonged" (ספר צחות)Note that as he is defining the actions of the mafsik, he talks about proper placing of disjunctive accents. The implication is the placing of a disjunctive accent as opposed to a conjunctive accent -- a melech as opposed to a meshares.
In this instance, however, we are not debating whether there should be a melech or a meshares, on any given word. All the melachim would remain melachim, and all the mesharsim would remain mesharsim, more or less. The question is which melachim should be placed, where different melachim would show that certain phrases are subphrases of others.
This is a function of the continuous dichotomy that we love to speak of, so often. However, it is quite likely that Ibn Ezra did not know about the principle of continuous dichotomy. Even though this was presumably a principle which guided the person or persons who originally developed the system and marked the accents, this principle was not known in medieval times. To cite Wickes, in a footnote on page 29, when discussing the principle of continuous dichotomy: "Jewish writers on the accents had no more idea of this law than they had of many of the chief grammatical rule. Its discovery is due to the unwearied diligence, with which the study of the accents was pursued by Christian scholars of the 17th century."
Shadal, then, would know of the rule of continuous dichotomy, as would Kogut, since both are after the 17th century. But Ibn lived in the 12th century!
As such, it is quite possible that he would see a bunch of melachim, properly separating off various phrases and subphrases. But lacking the idea of continuous dichotomy, it was equally admissable for al-pi Hashem to bind to lemaseihem as to vayichtov Moshe.
Thus, this is not necessarily Ibn Ezra diverging from trup intentionally. And we should examine the other example in Shadal and elsewhere with this in mind. He may be remaining (in general) true to his position that one should not diverge from the trup.