Paul, Here is a great chance for me to recommend PJ acquire you folks a nice cannon net system!

($$$)
Outside of the hunting season (which includes the methods involving shotguns) I've only captured turkey
with nets. You can go the traditional rocket net route, which involves some gunpowder or use the "netblaster"
style system that WCS sells which is a pressurized air system. Either will cover the distance and range necessary
but you are going to lay out some coin for that.
You might have luck with a drop net system which can be cheaper, same concept with a baited location, but
the net drops from poles above, can't see why a large enough net wouldn't do the same as from the rocket, but
in a more controlled fashion.
I realize most jobs don't entail one of these expensive options, but they are good to have on hand if you plan
to become more involved in the type of critter that might be streamlined with it.
Did I mention $$$....

**Another thought if don't plan to make these into a table fare or donate to soup kitchen, there are some good
chemical immobilizers that can be put in baited station that will allow you to basically walk out and pick up these
turkeys, just need a local veterinarian to work with and I imagine you might just know a few.
Again, only if state law allows and consumption isn't an issue. Used on urban ducks and geese an awful lot by
G-men.