I figured out the first stanza last, and I'm least sure about the explanations for this set of words. You'd think you'd need to nail this down to get a solid foundation for figuring out the rest of the poem, but...well, here goes.
To start, I'm strangely missing.
RHYME - This poem has barely any rhyming lines, and there certainly isn't a rhyme in this line. And for those of us struggling with this puzzle, it may have seemed to lack “rhyme or reason" (make no sense, have no logic).
Modified, I'm what a silly chef lacks.
THYME (modify by replacing R with T) - Maybe the chef is punny and has neither the herb thyme nor time to prepare dishes.
Again, and I'm subtly present.
THEME (modify again by replacing Y with E) - @Bailey already mentioned that there's a theme or motif within this poem.
Do me harm, and I'm perhaps you.
THEE (harm by removing M) - The objective case of the word “thou", an archaic form of “you"
With a change, I'm tall and resilient.
TREE (change H to R) - Both words can describe a tree.
Again, and this is certainly that.
FREE (change T to F) - This poem is an example of free verse, having no pattern in rhyme or meter.
Again, I'm a guitarist's worry.
FRET (change E to T) - Part of a guitar as well as a synonym for “worry"
Again, and I'll make a stand.
FEET (change R to E) - Organisms with feet stand on them. For the poem motif, they are groups of syllables in a meter.
Again, and our paths will cross.
MEET (change H to M) - To cross paths is to meet.
Again, and I'm some kind of kind of cat.
MEER (change T to R) - cat -> kat -> meerkat (an animal)
Adorn me, and I'm also strangely missing.
METER (adorn by inserting T) - This poem doesn't seem to follow a meter, a pattern of stressed and unstressed syllables.
Enrich me, and I'll destroy everything.
METEOR (enrich by inserting O) - A collision with a meteor is very destructive. Ask the dinosaurs.
Destroy me, and I'm a secluded commander.
REMOTE (destroy by rearranging letters) - A synonym for “secluded" as well as a device that can command or control other devices
Chop me down, and my feelings are obvious.
EMOTE (chop by removing R) - Word for showing feelings
With a swap, I've been judged.
SMOTE (swap E with S) - Possible punishment after judgement, especially from a deity
With another, I'm a torrid remainder.
SMOKE (swap T with K) - What usually remains after something torrid like a fire
And with another, I'm a torrid beginner.
STOKE (swap M with T) - What one does to start or feed a fire
And a last, you'd better turn me.
STONE (swap K with N) - From the idiom “leave no stone unturned"
Top down, I'm virtually nonexistent.
TONE (remove top or first letter) - This poem doesn't seem to have a tone or mood, besides a puzzling one.
With a flip, you can find me within.
BONE (flip by swapping T with B) - As human beings, we have an internal skeleton of bones.
Decorate me, and I'm a young helper.
BONNE (decorate by inserting N) - French word for maidservant
And again, I'm a soft, brimmed hat --
BONNET (insert again with T) - Yup, it's a type of hat.
One more change, and this is certainly not that!
SONNET (final change by swapping B with S) - A 14-line poem of a specific scheme, which this dynamic puzzle poem isn't.
Overarching motif is
this is a poem about a poem or prosodical terms: rhyme, free, feet, meter, tone, sonnet. Despite my name's meaning - no, really, part of it means poem - I'm unable to explain further at the moment. Sorry if I missed any details or just missed.
My mobile device is ill suited for composing this answer.