Many types of bamboo are terribly invasive. I will guess his is if he used tubs? Portland is a great place to live horticulturally.

Whatever you pick I recommend a mixed border so if a hypothetical emerald whatever borer comes by you don't lose the whole thing.

you dont have room for multiple trees .. as per your title ...

do you have patio furniture yet.. a table with an umbrella.. might do what you want done .... also.. by the time you sit down... you shouldnt see past the fence ...

i guess i am suggesting you get the patio set.. and see if and how that changes your variables.. before choosing the plants ...

ken

You have a huge fence there as is, are you on a slope where your neighbors are higher up and can see in your yard? Otherwise I don't see why you need a 'screen' of trees for privacy...maybe attach trellises to the fence and grow some clematis?

I don't see any reason for a hedge.

Plant something small in the corner, like a Jap Maple, or Redbud, will give you some shade, and looks pretty!

Is the goal to hide the fence? Do you need screening in the winter? I hate it when people suggest a shrub when a tree is asked for...so how about a perennial? A row of Baptisia australis...a really tall perennial with attractive foliage and flowers. You could easily trim it if it had too wide a foot print.