I recorded my voice saying “button” in American English.
Could you please tell me if I am saying it correctly?
(Native American English speaker here, Midwestern accent, also known as “General American”.)
I think you basically got it.
You’ve got the glottal stop for the tt, and I think you’ve even got your tongue in the right place, positioned to make a proper t as the glottal stop begins but not actually doing it.
You’ve also got a truly vocalic n. That’s probably the hardest thing to get right, or to believe: that the n really is the vowel for the second syllable, with no vowel between the tt and the n.
It sounds like you’re experimenting with a lot of variations, so this comment might be irrelevant, but there shouldn’t be much delay between the glottal stop and the n. In a lot of your experiments, you inserted a pretty long delay.
Also, the stress should be clearly on butt- and not on -on. There shouldn’t be much effort in the -on. Also, it’s excellent that you’re descending in pitch from the butt- to the -on. If you really want to sound American, try experimenting with a wider interval. In a sentence, of course, these pitches will vary, but as I’m saying button to myself over and over right now, there seems to be a drop of a perfect fifth from the first syllable to the second! I could be wrong about that, but checking against a piano, my pitches seem to be: F3 to B♭2. I think you’re basically going from around E3 to C3. You should probably listen closely to a recording of an American saying button (out of context, not in a sentence), take note of the pitch, and then experiment some more.
For comprehensibility, correctness, and clarity, your rendition leaves nothing to be desired. The only thing “Unamerican” about it is the pitch, and even that’s pretty close.