Alkanadi, unfortunately you still haven't understood the concept of transitivity. It is not important whether an actual accusative appears with a verb, but whether a verb can't have a direct object (something that can become a subject in a passive clause) with it (=intransitive) or it can (= transitive).

The expression mi finis is not intransitive, the direct object (e.g. mian paroladon) is just not expressed. If Z said mi finiĝis he himself would have been the object of this "ending", so something like I'm finished/I'm a dead man.

Verbs in E-o are either transitive or intransitive. Whereever it does not seem like that, you have either 1. an error, or 2. a use that only looks different at first glance, but still is correct, or 3. a homonym/polysemous verb.

The last case are e.g. fumi 1. 'smoke' (of smoke, intr.), 2. 'smoke' (a cigarette, tr.) or bati 1. 'beat' (hit someone, tr.), 2. 'beat' (make a beating sound, intr.).
These cases are mostly taken over from ethnic languages, but they are Fundamental and belong to E-o from the beginning, just like the polysemy/homonymy of e.g. artikolo (1. in grammar, 2. in a newspaper, 3. in a storehouse), and there is no use contesting or fighting this fact.

Alkanadi:

erinja:I don't recall seeing anywhere in the Fundamento that each verb must have only one transitivity, ever.

I don't recall seeing that either. I think verbs are supposed to have both transitivities since that is how it is used in the fundamento.

No, that doesn't make sense, and in fact if that were intended then we could throw the ig and igx endings in the trash.

The way the Fundamento works is that you have the Universala Vortaro (it doesn't have definitions, only translations of words into French, English, Polish, German, and Russian) and the Ekzercaro (with sample sentences). Transitivity is not given. For that matter, grammatical category is not given (noun, verb, etc) Rather, words inherit transitivity from the base languages (and category; we know bov' is a noun root because it is translated by nouns in the five languages). This is how Esperanto words "inherit" transitivity from source languages, and how they "inherit" multiple definitions. It doesn't mean you can apply any transitivity to any word, it means that Esperanto is a product of European languages and tends to behave like a European language in some ways, including in the fact that most words have only one transitivity but some are both transitive and intransitive.

it's just a category of verbs that is very small

By this standard, couldn't someone say that English is regular as well? English just has a lot of categories.

No, not at all. I don't mean category like a grammatical category that needs special treatment, I mean an informal grouping that someone might use for their own convenience as a student or speaker of a language, such as "words that begin with A" or "words that have more than one definition" or "words that have different transitivity in Esperanto than in another language"

Everything that Kirilo81 says is correct and helpful too.

Maybe this whole misunderstanding is due to the fact that some Esperanto verbs are inherently (semantically) causative and others aren't.
La soldataro marŝis norden.
La soldataro moviĝis norden.
Both marŝ' and mov' refer to a change in position. However mov' is semantically causative (to cause something else's position to change) and marŝ' isn't (to change one's own position by moving your feet in an orderly manner.)
Same with fum' (intr, ellasi fumon) and fum' (tr, ardigi). The transitive fum' (Mi fumas cigaredon) is an unmarked causative.

Just a wild guess.

And now I remember why I hesitate asking questions about languages. I wasn't trying to spark a debate over the proper use of Esperanto or even whether a given verb is transitive, intransitive or something else. The idea of inheritability of its x-itive nature from the source languages is interesting; however, my question is much simpler:
Which is correct / conveys roughly the same meaning as the English phrases.

To that end, are these correct?
The apple is dry. / La pomo sekas. (La pomo estas seka.)
John dries the apple. / John sekigas la pomon.
The apple is drying. (as in dried apple slices) / Lo pomo sekigxas.

ludomastro:And now I remember why I hesitate asking questions about languages. I wasn't trying to spark a debate over the proper use of Esperanto or even whether a given verb is transitive, intransitive or something else. The idea of inheritability of its x-itive nature from the source languages is interesting; however, my question is much simpler:
Which is correct / conveys roughly the same meaning as the English phrases.

To that end, are these correct?
The apple is dry. / La pomo sekas. (La pomo estas seka.)
John dries the apple. / John sekigas la pomon.
The apple is drying. (as in dried apple slices) / Lo pomo sekigxas.

Yes. All three are correct and unambiguous.

erinja:...in fact if that were intended then we could throw the ig and igx endings in the trash.

Would you have to throw them in the trash?

Doesn't La pomo sekas and La pomo sekiĝas have two separate meanings?

It seems that Modern Standard Esperanto is different than the original version.

Alkanadi:It seems that Modern Standard Esperanto is different than the original version.

No, seki, sekigi, and sekigxi did not have other meanings a hundred years ago.
But in early times in fact the stative verbs were not used very often, instead of seki Zamenhof would probably have said esti seka.

There are two other marginal aspects of the accusative with intransitive verbs I have not mentioned above:

4. The accusative can appear instead of a preposition: Mi ridis je/pro lia naiveco = Mi ridis lian naivecon.

5. There is a structure taken over from ethnic languages, which is called "cognate accusative" or "figura etmologica": An intransitive verb can role as if it were transitive in combination with a noun, which is semantically (and ideally also formally) cognate and has a qualifier with it: plori krokodilajn larmojn, ni iru la vojon celitan (Z).

Kirilo81:

Alkanadi:It seems that Modern Standard Esperanto is different than the original version.

But in early times in fact the stative verbs were not used very often, instead of seki Zamenhof would probably have said esti seka.

Using esti is probably the style I will use. It seems like a good one-size-fits-all solution.