If you must put your cats outside maybe you should look into purchasing an enclosure of some sort. Revival pet makes this really cool net to cover your yard so that the cats are safe. Try them in a crate outside in a shady area. My cats go outside to go potty and then I let them back in. You can’t just do it cold turkey. It sounds like you are dedicated and going about it in a caring way. There is alot to be scared of outside, such as wildlife, dogs,vehicles, airplanes flying overhead, etc… Good luck with them.