While we had the same the same criteria, private pool, GC or Orient and a view, upon touring many villas, we gave in and decided to get the best bang for the buck and went into the lowlands.
Much more grand, well kept, almost all gated. We did decide on La Favorita which blew our socks off and the housekeeper was the icing on the cake, She was a joy to meet and I'm sure she will take great care to watch over us.
Not crazy about the 25 minutes drive to GC especially through driving Sandy Ground but may split evening meals by going south including Marios, Jaxs and Jai's Contemporary Indian and a private chef.
Not sure I can make recommendation for only 2 guests as we are going with another couple.
We did find a couple villas in the lowlands but was missing the view, I think one was La Pinta along with it's sister property.
Maybe check the happy bay villas as I think they were a possibility while we were only looking for 2 guests.