Are these up to date photos? It looks damn clean in there already!
I'd just toss the old bedding into the run and call it a day. If you don't want them playing with the straw, then put it out for yard waste pick up or compost it.
No water, dry is best. I would also advise against the permethrin - what would you be treating for? Permethrin is not a preventative for pests, it only treats active infestations and you did not mention having one. It kills beneficial insects like bees as well.
I'd just toss the old bedding into the run and call it a day. If you don't want them playing with the straw, then put it out for yard waste pick up or compost it.
No water, dry is best. I would also advise against the permethrin - what would you be treating for? Permethrin is not a preventative for pests, it only treats active infestations and you did not mention having one. It kills beneficial insects like bees as well.