i'd keep the hemlocks healthy, they give you year round screening from .... squirrels? not sure who is looking at you. knowing this could help us give you better suggestions.

I'd take down the hemlocks and put up a fence. The hemlocks haven't been properly pruned for privacy, and they aren't the sort of evergreen that can be rejuvenated.

If you have deer, forget about arborvitae.

Depending on where you are, and if you require winter screening, there may be other tricks to play.

Consider adding Leucothoe popuilifolia or Mahonia beali in front of the hemlocks.

Below are options using Little Gem Magnolia & Bottle Brush Buckeye (deciduous)

What about building a simple decorative arbor/pergola over the walled courtyard and using curtains for more privacy when you want it. That could look sharp.

"The pics do not completely show all of the gaps/holes in the trees." But the point of pics is to SHOW the problem. If we can't see it, it's hard to evaluate.

Usually, where trees are used to screen, the lower level screening becomes worse over time as the lower branches decline. I wouldn't particularly care for filling the foreground (strip of lawn area) with screening plants. I think it would be better to keep it at a distance. You could replace the lower hemlock branches with the foliage of a shade tolerant hedge. I also wouldn't care for a privacy fence in front of the hemlocks. If you use a fence, it should be behind the hemlocks, close to the property line.

agree w/ mad_gallica. If the hemlocks aren't doing what you need them to, it's a tight space. Yank 'em and put in something (fence, hedge) that will work.