I recommend an OBi202. It supports Google Voice and can connect two phone extensions. So, you'll have these options.
Then setup a PAYGo account with a VoIP provider, add some funds, get a temporary number/DID, and build/prove your solution. When you have it working on your ISP/LAN to your satisfaction, ask that provider to port your number from COX. Do not cancel anything at COX. Integrate your ported number into your VoIP solution. When you have it working, go live. Discard the temp DID later.
I recommend
VoIP.ms for a provider... feature rich, reliable, low cost, and good for learning. CallCentric is another. Anveo is another. Google Voice can be good for free outbound failover, or more if you can live with it.
My notes document my OBi202 and
VoIP.ms solution. A good reference if you are actually trying to learn BYOD VoIP. If you get this far, you'll probably port (or cancel) your second COX number.
Why is your COX Internet not so reliable?... maybe that can/should be improved, especially if it's on your side. My COX Internet is very reliable. What model modem are you using?
OE