You are entirely correct, tutissimus is a superlative adjective that modifies the implied subject of ibis. No other reading is possible, as it is clearly in the nominative. Your “incredibly literal” translation is correct, the subject of the sentence is “the most safe you.”
Now, since I am assuming you have trouble putting the meaning together (the question is actually lacking, but let me assums so), this is one of many points where English, with its strict word order, and Latin, which is much freer in this regard, disagree. Semantically, the adjective in most Indo-European languages serves two distinct roles, but these roles do not always translate to the level of syntax or morphology.
First of all, an adjective can indicate a “static” property of the noun it modifies. This is called the attributive use. This adjective nominally attaches the property to its noun, without a direct relation to the action expressed in the predicate. In “Unnatural deeds / Do breed unnatural troubles,” both uses of unnatural are attributive: they modify deeds in the subject, and troubles in the predicate, by attaching a certain property they possess, and the verb ties two units together: X causes Y, where X is “unnatural deeds” and Y is “unnatural troubles.”
Second of all, an adjective can inherently be attached to the predicate, and this implies the modification of the noun not to be an unqualified property of the noun it modifies, but rather indicating that such a property arises as the result of verb action, or the truth value of the predicate. Unsurprisingly, such a use is termed predicative. In “chambers will be safe,” the adjective safe is not applied to the noun chambers unconditionally; rather, it is the action of the entire predicate: X will be Y X', where X and X' are chambers, and refer to the same chambers indeed, and Y is safe. chambers are not merely safe; they become safe by the action of the verb, which is a simple stative form of the verb to be.
Different languages imply different means to distinguish the two uses of the adjective, and some of them do not care at all. Let me digress into this for a moment. As English expresses the definiteness with an obligatory article, classical Latin does not have a syntax, or a special article word, to indicate a definite or indefinite noun. When a disambiguation is required, additional words can be used, and their repertoire is not wanting in Latin. While English has a and the, they are not adequate to express the semantics of, say, aliquis, which is “a certain (something),” a thing which is a-the-thing, in a sense; Latin morphology has unparalleled concepts, but Latin syntax has no such concept at all.
Having said that, English has a syntactic-only distinction between attributive and predicative adjectives. You can clearly understand the difference between our “Unnatural deeds do breed unnatural[ADJ.ATTR] troubles” from “Unnatural deeds do make troubles unnatural[ADJ.PRED].” Both make sense, and are grammatical, and this sense is different. Other languages go a step further, such as e. g. Old Russian, which not only had distinct morphological forms, i. e. different words with the same stem, but distinct endings, for the attributive add predicative adjectives, but also required different syntax (cases) for their use: a predicative referring back to the subject regularly disregards the agreement, and takes the instrumental. Latin, on the other hand, is lax in this regard, and does not distinguish predicatives in most cases (this is not universal; a double infinitive construction where the first argument may be the noun, and the second the predicative attached to that noun; but this is not a clean predicative case, which, as its central example, implicitly connects the modification to the subject of the predicate).
So, while "you will be happy" is a perfectly valid predicative sentence, *"happy you will be" is not, unless the speaker is Master Yoda. As a rule, attributive modifier is placed after the verb of the predicate. This is just not so in Latin, which, AFAIK, does not treat predicatives from attributives syntactically different. Thus, this literal "happy you will be," laetus eris, would be a perfectly valid Latin sentence.
Finally, the context is the king. All languages are ambiguous, but the ambiguity is normally resolved when a sentence cannot be understood in a different way. Unsimple, muti-word clauses allow literally hundreds of possible syntactic parses, but we the speakers somehow know to reject nonsensical ones immediately. In your example, a speaker automatically, without any effort rejects the reading "the safest you will go in the middle," as "the safest you" does not make any sense: there is only one "you", so the qualification makes no sense. But another reading, "by going in the middle, you [that single you!] will become the safest of [an imaginary continuum of all future states of] you," makes sense, and is selected effortlessly by the speaker.