Learn English – Other ways of saying “except for one”

The OED’s second definition of infinite is, when it is used with a plural noun:

unlimited or indefinitely great in number; innumerable, very many, “no end of”

There this supporting citation with ways from 1775:

Thus there are . . . infinite ways of being vicious, though but one of being virtuous.

However, the entry describes this use as being now archaic or rare. It is probably best avoided for that reason and because, as the other answers show, its use is controversial.

In the example, an infinite number of ways is preceded by There are rather than There is because an infinite number of premodifies the plural ways. This contrasts with the infinite number of ways, where singular number is the head of the noun phrase and so would require singular agreement.

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.