I have this problem as well. I hope you will post again with what you found helpful.

I like the commonsense approach suggested by Thunder Bow; maybe by taking the panic component out of it, I can realize that it's just part of the brain's job.
I wish I like tea; there seem to be so many with soothing properties!

Some things I found helpful for myself:

I stream some non-challenging, "comfort food" type of sitcom (generally, Golden Girls). I know all the episodes, there is nothing surprising in them to me, so they are basically nonthreatening background noise that drowns out the repetitive, swirling thoughts.

Playing white noise sounds: rain on a tin roof, rain on a tent (some great videos on youtube);

soothing music (again, just keeps a steady, harmless tone - something like Brahms lullabies).

On the dbt front, counting (deep) breaths; also, much like Thunder Bow mentions, acknowledging that I am having cycling thoughts, telling myself it is ok, and deliberately turning my thoughts towards some soothing imagery (mine is warm cabin in snowy woods; quiet, calm).

I've had to work a little to find some things that will work for me; I also have auditory hallucinations (mostly "many voices whispering") that make it hard to sleep, and make me afraid to fall asleep sometimes.