First of all, the fact that you call it "essay" already shows why we're not on the same page. SE sites are Q&A sites: you post a question, and then a variable number of users will give you an answer to that question. Both can be long or short but you're not posting an essay, you're posting an answer. There's nothing wrong with an answer being long as long as whatever is inside is related to the question and since questions on SE are meant to have a narrow scope, answers aren't going to be that long because of that.
If you ask a broad question, as is your case, then of course answers will have a lot more to cover, but the problem here is not the answers per se, it's the question. We have a close reason for broad questions because SE sites are meant to answer a more or less narrow topic.
The same applies to "discussion": this is not a forum, there are no discussions, or at least, there aren't any of the same type as those you could find on a forum board.
One of the essays, on the question of intermediate forms in phonological derivations, has not yet been attacked. It is here: Eliminating intermediary forms to account for production and perception. The other essay, on the question of describing grammatical relations as differences in level (in a certain sense), which has been put on hold, is here: How can PSG describe the vertical dimension of sentence structure?.
"Attacked"? Maybe you shouldn't use loaded words, there was no attack. I'm just enforcing the rules of a website I've been called to supervise. The question I closed was called to my attention, the other I didn't see until now. I have and it seems fine, but your answers should be reduced to a single answer: just focus on the point of the question, you don't have to present a paper based on it. Just answer the question.
The official reason cited for putting the second essay on hold was that it is "too broad", specifically "There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs." I'm not aware of any other answer that has ever been given to describe the factual instances of levels I gave in the third section of my essay (the answer titled Vertical levels), for instance the predicting of precisely five types of English auxiliary verbs. So I guess what is meant by the "too broad" objection is that "good answers would be too long for this format".
Your guess is wrong, good answers are scoped, concise, to the point and while providing some context, they do not become essays. That's what the close reason means.
But actually each of the answers I gave (corresponding to sections of the essay) is quite short. In the comments to my question, two commenters suggested that I reformat my essay as one long answer, as a remedy to the defect they saw in what I wrote, but of course that would make the new answer rather long. So how could that fix the problem of a question requiring a long answer? This does not make sense.
Again, a long answer is not the problem if it's necessary to answer a well-scoped question. If the question is OK and you need to give a long answer to cover it, then so be it. I have given long answers myself, but if the question is asking about everything and you give an answer that can easily be made into a paper, this is the wrong place for both the question and the answer. All SE is asking you is to narrow it down.
One commenter implied that I shouldn't provide multiple answers to my own question, but I see nothing in the site help files to prohibit this. Did I really break a rule?
One commenter said that the sections of my essay would be viewed in random order instead of the order I intended, but I pointed out that this is not so provided a reader clicks on the "oldest" option at the end of the question. In any case, this seems irrelevant to whether my question is really "too broad".
Multiple answers by the same author are rare, it really depends on the question and each case. Typically, there is no need for more than one answer per user, especially on a site like Linguistics. On a site like StackOverflow, this might happen since you provide two different solutions to one problem, for example using different programming languages. But here, there is no case that comes to my mind that could justify that.
Narrow down your question and reword the answers to fit in one. If you really don't want to lose all that material, start a Linguistics blog and you can even link to it from your answer for "additional context". There was the possibility to create blogs on SE sites, but apparently it has been discontinued. If you want to create one for Linguistics SE, I won't be opposed, and on the contrary, I think it'd be a nice idea. You can try contacting SE directly and see if something can be done. Of course, this means that you should commit yourself to it.
Merge the answers on the other question, which doesn't seem broad to me, and that's why I'm not closing it for now. But you should merge the answers.