Case after 'except'?

One can use 'except' as a preposition, as in the following sentence:

I gave everyone except Mary a present.

Changing 'Mary' for a pronoun we get:

I gave everyone except her a present.

Clearly the following is wrong:

*I gave everyone except she a present

So my question is: does except always take the objective case in English? Consider the following sentence:

All except him agreed

To me, "he" sounds more elegant here, so maybe the noun affected by 'except' keeps the same case it would otherwise have in the sentence. But then:

Except I, we all agreed

sounds definitely wrong compared to "Except me, we all agreed." Perhaps it is not a matter of case at all, but something else? I found this question very hard to google for, so that's all I've got to bring to the table.

Except can be a preposition, conjunction, transitive verb, or intransitive verb.

The Merriam-Webster Learner's Dictionary has a great page on except.

In your sentences above, you are using except as a preposition, so it should take the objective pronoun.

Probably the reason you dislike

All except him agreed.

is the order of the words--him sounds awkward before the verb, even though it's not the subject. If you change the order, without changing the meaning, you get

All agreed except him.

which you probably will not find awkward.

So the short answer to your question is that when except is used as a preposition, its object, if it is a pronoun, needs to be in the objective case.

The M-W Learner's Dictionary page gives examples for sentences where except is used as a conjunction, where the pronoun later in the sentence is the subject of a phrase, so it is in the subjective case:

I would buy a new suit, except I don't have enough money.

In this situation, except is a conjunction, and the second "I" is the subject of the second statement. So while there are times when the word except will be followed by a subjective pronoun, they are different situations from your examples.