'Green Giant' is a horticultural hybrid involving an Asian species, for a natives only project you would choose Thuja plicata instead - if using a tree of this type at all. Also the native species is better looking.

What is growing in the exact spots you want to plant now? Often areas directly beneath large maples are too tough for much tree or shrub growth. What has managed to grow there previously indicates what future possibilities there are.

Otherwise: any idea why the one tree was taken out? Many Big-leaf maples in this region are having problems in recent years - for instance I've seen on the order of a dozen of them - most of fair size - die in the last few years in just one part of a friend's Island County property.

Bigleaf Maple Decline, Update and Next Steps

https://dnrtreelink.wordpress.com/2016/08/10/bigleaf-maple-decline-update-and-next-steps/

If it turns out the whole grouping next door is on its way to removal you don't want to plant anything that will be in the way or destroyed when the rest of them come down.

The neighbor claims the tree had damage to the crown, but I really think he just wanted more sun (long story). Growing now are Indian plum, red huckleberry, salal and sword ferns. I agree with you that the height of new evergreens growing into the crown of the maples presents a problem. However, he is uphill from us, so I need something that is at least 15' or so, and also has about a 10-15' spread. Thanks for your comments.

If you can drop the native restriction and provide water in summer one of your best bets would probably be Fargesia bamboos. These can be quite nice, grow in shade and won't take 20 years to size up.

If instead the natives only restriction is set in concrete then about the only choice you have is Thuja plicata. Local shady woods with vegetation containing species such as those you have listed as being existing have no bushy, attractive native evergreen species of more than shrub height other than this conifer - it is the only kind that looks like it would lend itself to serious screening of views.

Where salal is present evergreen huckle-berry may certainly also be possible - these two often grow together in the wild, on those occasions when the Vaccinium is present at all - but unless stimulated with liberal watering, this latter, like other heaths including the salal can be quite slow- and rather small-growing, prone to weevil attacks beneath overhanging trees and so on. And lack density in heavy shade, as do most trees and shrubs.

Finally it is often the case that when people ask for quick 15 ft. tall plantings to block something next door they are thinking in terms of this screening being over near where the source of the unwanted view is, want therefore such height. But they may not in fact be using that part of the property most of those times when they are wanting there to be a visual barrier present. So that installing a source of relief near where they are looking from instead, well inside their property would be more efficient - and perhaps even immediately effective, if an architectural feature or modification is used.

I also live on a heavily wooded lot on Bainbridge. The vegetation surrounding my property consists of bigleaf maples, the native western red cedars (Thuja plicata) Doug fir, a few wildling cherries and the odd madrona. And the usual lower growing natives.......salal, both deciduous and evergreen hucks, mahonia, ferns and assorted Rubus species.

You can see the thujas growing right next to the maples - in some cases, almost on top of the maples - however most of these have seeded themselves. Planting anything of significant size now within the root zone and canopy spread of the maples will be tough. I'd agree with Embo that it might make the most sense to address the screening issue in some other manner within your property line or at a distance from the maples so their competition for sunlight, soil nutrients and water is not so fierce.

Planting closer to where you need the privacy rather than adjacent to the remaining maples has other advantages also. Trees that old and large regularly drop large branches that are liable to damage any tree planted under or near them.

Sheer window curtain block the view from a neighbor as long as you're not standing very close to the window.