I'm not implying you weren't experiencing issues, but as a counterpoint, I paired my iPhone 7+ with BT first then started using CarPlay and it's working fine. Sometimes I see the bluetooth connect for a second then disconnect when CarPlay starts up, right at the beginning of a drive, but other than that the bluetooth connection is ignored while CarPlay is active. I have a 2017 Hybrid EX-L if that's relevant.Have you paired your phones with Bluetooth or just plugged them in and set up AA/CP with no BT connection. Reason I ask is I was always pairing my phones and then setting up AA/CP and had lots of issues such as you're describing.
I reset my HU and didn't pair anything. Carplay has been near flawless since. I think there's a conflict for priority if you BT pair.
I'm not sure it matters though, I setup the bluetooth connection thinking I might not always plug my phone in, but I really like CarPlay and use it exclusively for my infotainment except if I listen to the radio or satellite, or if I want to look at the trip computer.