I would NOT move this nest. Why can't you delay some of the
activities that might disturb the bird? I made my pruning
schedule flexible this year because some bushtits hung a nest
from the bottom of some weeping willow branches that I usually
prune up out of the way. The consequence? I've had to duck
under the branches when mowing the lawn underneath. (Amazingly,
these birds fed young in the nest when I stood only a few feet
away while mowing - but they were not disturbed like this very
often.) I purposely left the entire tree unpruned so attention
would not be drawn to the part with the nest. I've also had to
delay pruning my arbor vitae hedge when I realized I had House
Finches nesting in it - and I've done that several different
years. If the timing of your deck job is at all flexible, why
not just delay it? Or, if your experience is that your activities
don't usually disturb the flycatchers, then just go about your
business and let the birds go about theirs.

--
Barbara Combs obie '70
Eugene, OR
bcombs at ednet1.osl.or.gov