Contrary to what some people believe, DE (Diatomaceous earth), will do nothing as far as controlling worm populations. Put simply, it's ineffective when wet, and in case you're unaware a bird's intestines are wet.
As mentioned above, DE can irritate the lungs of our respiratory sytems. Did you know birds have very sensitive respiratory systems, more than us (?) If we're supposed to were mask handling this stuff why are we putting it in their feed? Actually, the IARC rates DE as a group 3 carcinogen.
https://www.osha.gov/laws-regs/standardinterpretations/1999-04-05#:~:text=Diatomaceous earth has been tested,the research conducted to date.
The carrots and cayenne are doing little for your birds as well. I'm unaware of any natural products for deterring worms in birds.
If your worried about worms, but don't want to unnecessarily deworm them, go collect a few fresh fecal samples, mix them together and bring them to your vet, and ask for a fecal floation. This diagnostic test measures the number of worm eggs in the feces and lets you know if there is an overabundance to the point where you want to treat them.
I perform several diagnostic tests here on the farm (Peripheral blood smears, urinalysis, gram stains, total plasma protein evaluations) as well as centrifugal fecal floations, which, as I stated above lets me get a good idea how many worm eggs each bird has instead of contributing to some of the dewormer resistance you're starting to see in some parasites. If you are interested in starting fecal flotations, just ask.