What about Blue gum Eucalyptus trees. They grow fast in your area and the aroma may cause some future nosey neighbors to keep their blinds closed.
Hard no on Eucalyptus trees. Not only are they invasive here they also can't handle the strong winds from storms in our area so the wind will knock them over. We've had lots of issues with them in the area between falling through fencing and falling into water tanks. Would highly recommend avoiding.
Oak trees are a good idea as they require little input once established and are native so they can handle the weather and wind here. They are a slower grower so I'd plant something taller for the meantime while they grow in. There are some varieties that don't lose their leaves in the winter too.