If according to Descartes clarity and distinctness indicate truth, are there forms of knowledge that escape his method entirely?

What we can express in words and what we can formulate as propositions, either what we can refer to as distinct facts (that such-and-so is the case) and also what we can describe (whether it's an object, an event, a process), is significantly "less" than what we can experience and perceive. I am able to recognize the sound of a violin or a clarinet, but I would be hard-pressed to describe those in a way that would make you say "Ah, you mean a clarinet!" (unless, of course, the choice is already constrained as in a multiple-choice test). This implies that there are indeed "truths", in the sense of conscious experiences, that go beyond what can be expressed distinctly in words.

Diana Raffman (quoted in Thomas Metzinger, Being No One - The Self-Model Theory of Subjectivity, p.69) put it like this:

It is a truism of perceptual psychology and psychophysics that, with rare exceptions, discrimination along perceptual dimensions surpasses identification. In other words, our ability to judge whether two or more stimuli are the same or different in some perceptual respect (pitch or color, say) far surpasses our ability to type-identify them. ... For instance, whereas normal listeners can discriminate about 1400 steps of pitch difference across the audible frequency range, they can type-identify or recognize pitches as instances of only about eighty pitch categories (constructed from a basic set of twelve).

This does not mean that those truths are not analyzable, though. Our experiences - also when they go beyond language - do have structure and function. They may be subjectively "immediate", but that doesn't imply they are not historically contingent, depending on being raised in a particular culture. Training plays a big role in what we actually experience.

Art itself can be seen as a way to "analyze" those truths. Training in art is a way to sensitize (and desensitize) yourself, so to also generally perceive sharper, even when verbal (or purely "logical") analysis seems impossible. A work of art is not simply an object of perception: it's an exploration of possible ways of perceiving and feeling.

Art is about the person's pleasure or displeasure being felt through experiencing the work of art. Since it is about feelings and presentational meaning, as the OP correctly points out, art or aesthetics (the Greek word for perception and sensation), then, involves the use of non-discursive symbols rather than discursive ones, different from those used in math, science, language, and logic. The latter is the focus of Descartes's Discours de la méthode (1637). Before producing this work, Descartes's first book was on the art of music in his Compendium Musicae (1618). Descartes argues that the purpose of art, and specifically music, is "to delight and to incite various affects in us." He explored the mathematical and physical principles of sound (like proportion, consonance, and rhythm) to determine which combinations were most pleasing to the senses. Essentially, when talking about art we are not talking about objects or the works being produced but the effects that such experiences have on us, as subjects. The beautiful, for Descartes, is defined as what pleases the most people. This is why Hume, Kant, and many other theorists of aesthetics argue that we take in the work of art disinterestedly. I would argue that some points discussed in this small work show up in what would be Descartes's last book On the Passions of the Soul (1649). Scholars have referred to Descartes's description of the emotions as a "visceral aesthetics": https://publish.iupress.indiana.edu/read/through-the-eyes-of-descartes/section/fff76010-cc66-419c-b290-59962eeb5d5f

The French enlightenment sage has interesting things to say about music and art, but did not provide a systematic, comprehensive treatment of it in the way his other works attempted to do, focusing more on the experimental method and the formalization of nature through mathematics and natural philosophy. Therefore, I think it is an overstatement to contend that Descartes's philosophy can be read or interpreted as being anti-aesthetics.

Aesthetics was not in Descartes' focus. He used the term truth in the sense of true statements which are part of a theory.

You ask about the term truth in a derived sense, as used in aesthetics. Descartes' method ("Discours de la méthode") does not apply to aesthetics.

Frame challenge: False statements can be perfectly clear, and perfectly distinct. (Note that if you think the preceding sentence is false, it becomes its own counter example to that claim, since I think it is clear and distinct. The worst you can say is that it is undecidable.)

Alternatively: On the third Tuesday of every odd numbered month, I become a small black alleycat. I grant that "become" may be argued to be unclear, but if I mean it literally...

Clarity and distinctness can be one mode of artistic beauty. It is not the only such mode. And beauty is not truth.

'Contrariwise,' continued Tweedledee, 'if it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic.'

According to Sanatan Philosophy Mind is part of an Metaphysical System known as Antahkaran. This System contains Heart, Mind, Ego and Chitta. Chitta is the nascent background where all the other metaphysical enyities come into play. Now Clarity is a property of this System, it manifests differently in these entities, Mind: Clarity of Thought, Clarity of Vision, Heart: Calmness, Ego: Confidence. Mind can see clearly but it can explain only part of it. Like yesterday I went to Mall with my two cutest munchkins, 5-6 years old so as we were driving through one was telling me my grandmother lives here, my mother works here, my dad works there, I CAN CLEARLY SEE INNOCENCE RIGHT IN FRONT OF ME, I KNOW, BUT IF YOU ASK ME TO DEFINE IT?!!!!! *Crickets...

In fact not one or two ALL MEANINGFUL THINGS IN LIFE ARE BEYOND MIND. Define Father, Mother, Kid, Friend, Love...

Mind or "known" is a minuscule part of World, Truth is Beyond Mind. That is why "proof" of God is useless question. That WHOLE DOMAIN IS BEYOND MIND, AND with "clarity" you clearly see that too.

But Clarity is very difficult. It is very important however, Knowledge is a function of Clarity, not Intelligence. Knowable Knowledge is Superset of Describable Knowledge. Mathematically or Logicaly Describable Knowledge is a smaller set still.

You ask:

If according to Descartes clarity and distinctness indicate truth, are there forms of knowledge that escape his method entirely?

Descartes method, sometimes called Cartesian skepticism (SEP), is that of rational dialectic with a healthy skepticism which settles on a foundationalist approach to knowledge, so any form of purported knowledge would have to be irrational and beyond truth, certain without reason, and unconcerned with reasoning deductively and certainly. Thus, an epistemiologist would have to look beyond types of knowledge that concern reason, science (in the broad sense), judgement, testimony, and doubt. One candidate for that is supernatural or divine revelation (SEP).

Both Scholastic Aristotelian thinking and Carteisan skepticism are fully compatible with God, but there are beliefs in approaches to knowledge of God that bypass Cartesian skepticism. One form of those, according to the SEP article is manifestational revelation (SEP), something like the Burning Bush. Another is non-inferential direct cognition (SEP) where God speaks directly to someone's mind. Both purported forms of knowledge are beyond reason and explanation, the former because it might be understood as some form of brute fact, and the other because it requires no inference. Knowledge is typically conceived of as justified, true belief, but both of these forms of knowledge simply bypass justification.

Of course, neither of these would be acceptable to a natural epistemology (SEP) like Quine advocated, and both might be defended by a religious epistemologist (SEP). Such sources of knowledge go beyond reason in some way and therefore are embraced by fideists (SEP). Both abandon the legacy of Descartes and beliefs that inhere to Classical Rationalism that Descartes helped found.