You could sterilize, clean out, and check each of your racks and clear them to be placed into another room. Once all your animals are out you can do a thorough clean of the room using pesticides or the non harmful methods as bogerthophis has stated. I would close the air vents to prevent spreading through the house, and manually clean the air vents of any spiders. I’d then take a though look around the room to see if you can find an opening on where these spiders could’ve entered, and seal any if you see them. Once you’ve sealed and cleaned the room, I’d wait about 2 weeks for it to air out and see if the spiders are really gone. If so, check your racks one more time and sterilize them again in case there might have been one or two remaining and then put them back into the room.
I know this would be extremely time consuming and take a lot of effort, but this will provide a higher chance of really getting rid of them and preventing a future problem. I know this might be a lot more difficult if an option, so you can choose other methods before you reach this one, but I thought I might just post it in case you want this as your last resort or something.
I hope you find a solution that works for you.