Yes, Elector PSP is supposed to work with one treatment. I've never used it due to cost, but in the link I gave you before, that is her preferred method and product. I would just make sure that you get good coverage, and I would repeat treatment if you saw any signs returning after a week or more has gone by.
I would guess that composting will kill them, if they can't find a host they will starve. I really don't know how far they travel without being carried by something. I suppose you could potentially carry them from the garden to the coop on your clothing or shoes, not really sure. I usually burn my used bedding. Putting it in sealed trash bags for disposal would also work. If you have enough Elector, you could spray that in the garden also. It's supposed to be safe for that, and there is no egg withdrawl when using on your birds. I've never found DE to be effective for anything, though I know many swear by it.
I would guess that composting will kill them, if they can't find a host they will starve. I really don't know how far they travel without being carried by something. I suppose you could potentially carry them from the garden to the coop on your clothing or shoes, not really sure. I usually burn my used bedding. Putting it in sealed trash bags for disposal would also work. If you have enough Elector, you could spray that in the garden also. It's supposed to be safe for that, and there is no egg withdrawl when using on your birds. I've never found DE to be effective for anything, though I know many swear by it.