Sold as horse fly and/or perimeter spray (at places like TSC or feed stores), a permethrin based product might work well. Permethrin is a very affordable synthetic version of pyrethrin a chrysanthemum extract.. noting that even the "natural" version is still poison.. also noting that it's approved for use on laying hens with NO egg withdrawal time when used as directed.. effective against lice, mites, etc.. comes in ready to use or concentrate. I don't think it's a repellent but it does stop proliferation, in MY experience. A less affordable but possibly still effective (I think natural) solution.. Elector PSP.
I first saw someone using it (fly spay) to keep flies off their cow.. when I started using it to help keep mosquitoes off my goats.. I just happened to have it on hand the first time my birds got lice or mites.
Not sure how high your humidity goes.. but DE is ineffective at external parasite control in humid locations like mine.
True story.. folks say mosquitoes are repelled by mint etc.. so I had some mint plants on my patio table and watched them land right on top and sit there happily.. maybe freshly cut or strong oil smells work.. but just growing.. nah, not in MY experience.
One "natural" thing that totally has worked and makes a big difference here on the nor-Cal coast.. a good breeze, even in the form of a fan or oscillating fan.
Hope this helps with some ideas.