You're almost there, a little bit of patience is all you need.

I'd just wait.

Maybe install a pop-up gazebo with curtains in the place of outdoor furniture.

I would still put up a fence, even if it is just 6 foot. It'll make an appreciable difference to noise compared with trees and will visually block moving cars. It will also stop people walking past from looking into your garden.

How do you use the part of the yard that you would lose by additional plantings? If a smaller green area that is private and peaceful is more appealing than a larger noisy public green area, why not go for it? Where are you located? Is this the best time of year to be planting mature trees? I'm in the southeast US and you definitely want to do that in the fall not spring almost summer.

I'd also work on changing out that bit of privacy fencing along the patio. I'd do something that an evergreen vine can grow on. Something like this but with vines on it. Seems you need something sound absorbing, not sound reflecting. I wonder if the solid fencing is actually capturing/amplifying the sound somehow. What is it made of?

Wood Lattice Privacy Screen with Round Wooden Columns · More Info

This is a picture of my side yard. That is a star jasmine vine growing on a four foot chain link fence and then over the top of my wood fence that faces the street. It stays green all year and grows like crazy. Very sound absorbing and visually and physically very dense. Plus it smells great when it flowers. That's only two plants that have grown over the years. I'm in 7b/8a. In fact if you can do a 6 ft fence across the road side and add a vine to it that grows up like this one you will actually have an 8 ft barrier.