Roofing it would actually be the most predator (and rain/snow) proof way to go, but I know that's not cost effective or ideal based on the set up sometimes.
HWC should work, but the depending on the climate the tarps might not hold up for very long, so take into account replacement costs. And you'll need to make sure to add structural support, as 50' long of any sort of wire mesh will add weight and may sag especially with the addition of any snowfall.
My run is topped with netting, which isn't as predator secure but does allow rain and snowfall to get through, which works for my climate.