If you can't install the strips singly, then tie them back to the sides, leaving the middle open.
I'd be out there harassing that Wren multiple times a day.
Great!
Can't wait to see it. Have read that installing a couple pieces at a time from the outer edges in helps acclimate the chickens to pushing past and thru the strips.
Did you remove the nest?
Still a Slippery Slope....and not a good suggestion.
The solution for the OP's situation is to remove the nest and exclude the wild birds from entering the coop.