About the only thing that I can think of (and it's aestetic not for screening) would be a Yew such as:
Taxus x media 'Beanpole' or Taxus x media 'Flushing'. I think 'Flushing' will give you the most "screening" but you'll need to plant it fairly close to your shed: It basically should be planted 1 meter away.

You 'know' you planted a tree that given time will fit that spot perfectly, in relation to the shed. What you're looking to do now is plant something that ultimately is going to crowd walking space between your shed and eventually your Serviceberry. That includes mowing. The positive aspect of a Yew is you can prune them any which way you want to, including down to bare-inner-wood and they will form new foliage. If it ever came to be that the cultivar 'Flushing' was 5 meters tall and one meter wide and you wanted to cut it down to 1 meter tall, you wouldn't do any damage to it.

For me, your plan should've included an evergreen screen behind the serviceberry and the serviceberry being brought forward to give it room away from the screen. If you were to move the servicebery (now or anytime the ground is workable) that seems to be the common sense route and gives you the opportunity to do the job, correctly.

Then you could plant, i.e., going from the shed to the left in the photo: (3) Thuja occidentalis 'Hetz Wintergreen' in a straight line and then begin to make an arc with a Picea glauca 'Pendula' then a Picea pungens 'Iseli Fastigiata' aka 'Fastigiata'.

That's my opinion, anyways...
Hetz Wintergreen first one 1 meter from your shed then on center every 1.5 meter.
Picea glauca 'Pendula' 2.5 meters from 'Hetz Wintergreen'
Picea pungens 'Iseli Fastigiata' 3.5-4.0 meters from P.g. 'Pendula'
This for a screen. You can make adjustments with the two spruces if you want to give them room not to touch.

Dax

why limit yourself to the property line???

you have already lost the battle at that point ...

if you have no plan for gardening.. in the next 30 years.. plant a maple.. half way between the property line.. and your house.. and be done with it ....

at the angle of your pic.. you sight screen will have to be 2 to 3 times the height of your shed... to barely get to window height ..... and to get that height.. AND REQUIRE JUST ABOUT NO WIDTH.. is not really going to happen..

you need a 50 foot tree.. in the middle of your yard ... dont you think ...

ken

Dax,

What kind of spacing do you suggest between the Thuja's & my serviceberry?

I agree with the suggestion Dax made...here is what it might look like...As Ken said, you would need a very tall screen to completely block the view of the neighbors, due to the angle... But, I think this would be a nice improvement.

Bring the serviceberry up quiet a bit, no reason to stuff everything right up against the property line.