FWIW, I didn't want to segregate my pets either, and never have. I understand how stressful it is. I almost died when my "tested cat safe" Loca walked into the house and grabbed my cat by the neck. I came very close to returning her, but was shamed out of it Finally one night I looked at her and realized that she was scared and from there on, she was here to stay.
I'm sorry if I seemed insensitive because I do know how you feel. I already had a resident greyhound when I adopted Loca, and it was still very tough. After a month of crating her when I wasn't home and keeping her muzzled and tethered to me, she really did change. She became very friendly, or even loving with cats.
You have to do what's best for your family and for Phaeton. Would it help if somebody from your adoption group was able to stop buy and assess the situation?