I wish I had a wonderful tip to give you about distinguishing quod from quod, but I don't. I get tripped up from time to time, though I can usually work it out in context. (Some helpful texts will mark tricky adverbs with an accent mark like hîc, "here" vs hic "this," similarly quòd).
But in addition to context, keep a close eye on syntax even though Latin likes to play fast and loose with word order.
Ibo ut, erus quod imperavit, Alcumenae nuntiem…
Notice that erus precedes quod which is a sign that quod is not a conjunction, which you can expect at the beginning of a phrase unless they are post-positives (which are words like "enim" "igitur," and "autem" which cannot begin a sentence; a word is either post-positive or are not, and you know that quòd is not).
Syntactically, it makes sense to have quod be a relative direct object here, stating "what the master ordered." As you pointed out, it makes sense to have a direct object pronoun here based on these verbs.
I translate the sentence "I go to report to Alcumena what the master has ordered." Changing the order of the clauses is a good idea in English, which doesn't like compounded clauses as much as Latin.
You can't switch the pronoun for the conjunction depending on preference. Sure, it may be that it's up to the interpreter (you) to decide, but there will be one correct reading which the author intended. “Ibo ut, quod erus imperavit, Alcumenae illud nuntiem” would have the possibility of a different meaning because of the new word order, as you point out. But you can only translate "quod" as because in this sentence, not the one from Plautus.
Sorry I couldn't give you a straight forward answer.
Horae quidem cedunt et dies et menses et anni, nec praeteritum tempus umquam revertitur nec quid sequatur sciri potest. Quod cuique temporis ad vivendum datur, eo debet esse contentus. --Cicero, De Senectute