I'm going to try another approach to answer your question. My answer is based on the explanation given in the book Meaning and the English Verb (2nd ed.) by Geoffrey N. Leech, which I remember you have.

Let's recap. In chapter one, Leech discusses the two main uses of the Simple Present: unrestrictive use and instantaneous use. The unrestrictive use is about state verbs (be, live, etc.) and eternal truths (e.g. Two and three make five.) The instantaneous use is about commentaries, demonstrations, and asseverations (e.g. I beg your pardon.)

In entry 11, Leech mentions that,

These PERFORMATIVE VERBS express formal act of declaration, in contrast to the Progressive forms We are accepting your offer, etc., which merely report the speaker's present activities or future intentions. This usage is also characteristic of more ceremonial contexts, such as

​　　　ship-launching: 'I name this ship . . .'
​　　　judge passing sentence: 'I sentence you to . . .'
​　　　card and board games: 'I bid two clubs.' | 'I resign.' | 'I pass.'
​　　　wills: 'I bequeath . . .'

After the above excerpt, Leech also mentions a bit more about the difference between I write . . . and I am writing . . .,

Also, in formal letters the verb write is sometimes used as a performative: I write to inform you that . . . (But in a more informal style I am writing . . . is preferred.)

In your example, I'm making you all personally responsible for his deliverance, I believe that the verb make is an activity verb (a type of event verb, according to Leech, see 36c), and it's more appropriate to use the Progressive aspect. Using the Simple Present is possible, but it will make the utterance sound ceremonial, which may not fit the context (the occasion in the movie--I haven't seen the movie yet, by the way. :-) as well as the use of the Progressive aspect.

Sgt Farell is informing the other soldiers, as he speaks to them, that they are all responsible for Cage's combat status. If he had taken the decision earlier, or if he wanted to inform them they already are responsible, he would've said "I've made you responsible for Cage's combat status".

Now, why not "I make you all responsible?"

I believe it wouldn't be technically wrong, but would sound very, very odd. One of the reasons for that — except for the one I mention above — is that "I make" can imply a continuous effect or routine:

I make pasta everyday

I make you tick, don't I? (this is the more important example)

Sgt Farell only has to make the soldiers responsible once.

Also, since make can be paired with a lot of words that can change its meaning, I think it's an exception. When you say "I advise", I know you're giving advice, when you say "I warn", I know you're giving a warning, but when you say "I make"....

Do you make it clear to your children they must brusht their teeth? Do you make it the office in time? Do you make an exception when your children give you a good enough reason not to brush their teeth?

Notice how in each of the three questions above, make has an entirely different meaning: In the first, it's an order, in the second, it's another way to say "arrive", and in the third, it's another way to say you can be lean with your children under certain circumstances. (or that you are spoiling them horribly ;))