I went with a PTZ initially, and found it's actually better to use 2 vari-focal turrets instead. So, I have not only the 2 turrets, but also a PTZ that can be triggered by any one of the turrets if they detect motion. It's very effective this way as it gives not only 24/7 viewing and recording of the entire yard, but also the ability to watch an intruder a little closer should the need arise. My situation is very similiar to yours with a narrow area between a detached garage on one side, and a patio and back yard on the other. If one of the turrets picks up an intruder, it will trigger an IVS rule (intrusion or trip wire) and swing the PTZ around to the area needed. Multiple zones in the turrets can be used, giving you a 'follow' effect of the intruder. Yes, it costs more, but the coverage given is well worth it. Note the turrets are AI capable so false alarms are at a minimum, as AI has effective filtering for human or auto. My setup has not only trees, but also a great deal of steam from the furnace in the winter. The steam causes havoc with false triggering on the older turrets I originally used. The AI cams have almost completely eliminated this. To get AI in a PTZ, the pricing starts to go up a lot.
To answer your question, in my opinion a PTZ is not ideal in your situation. But, only if you need to cover the side yard enclosed by the fence. If You want to cover just the back yard, it may work out OK.