startBrowsingForNearbyPlayersWithHandler() in iOS 8 in Swift

I'm currently making a 2-player strategy board game in Swift and need to connect two iPads over local WiFi or Bluetooth. No matter what I've tried today, I can't get them to detect each other (I've tried over local WiFi and Bluetooth).

Here is my authorization code which runs in the UIViewController when my app first launches (which always returns "Self local player is authenticated." along with the ID:

private func authenticateLocalPlayer() {
    var localPlayer = getLocalPlayer()

    // If Apple were doing their job right, this is what the proper code should look like:
    // var localPlayer = GKLocalPlayer.localPlayer()

    if ( !localPlayer.authenticated ) {
        localPlayer.authenticateHandler = { (viewController : UIViewController!, error : NSError!) -> Void in
            NSLog("Error: \(error)")
            if viewController != nil {

                // Authenticated?
                self.presentViewController(viewController, animated: true, completion: nil)
                NSLog("viewController is not nil")
            } else if (localPlayer.authenticated == true) {
                NSLog("Self local player is authenticated.")
                NSLog("My name is \(localPlayer.playerID)")
            } else {
                NSLog("Not authenticated")
                NSLog("Player is \(localPlayer.playerID)")
            }
        }
    } else {
        NSLog("Player is already authenticated!")
    }
}

and here is my code to detect nearby devices in a separate UIViewController:

override func viewDidLoad() {
    devicesLabel.text = "Waiting for devices..."
    searchForDevices()
    NSLog("Ran searchForDevices()")
}

private func searchForDevices() {
    GKMatchmaker.sharedMatchmaker().startBrowsingForNearbyPlayersWithHandler() {
        var status = $1 ? "true" : "false"
        self.devicesLabel.text = "Reachability changed for player \($0) with status: \(status)"
    }
}

No matter what I do with my two iPads (both are model iPad 3), neither one ever sees the other. Am I calling startBrowsingForNearbyPlayersWithHandler correctly?

Also notice that in the authorization code above, I'm using the Objective-C workaround recommended by this post: Game Center not authenticating using Swift, since the "Swift way" of doing that didn't work for me either.

I also ran Spelltower across both devices over local WiFi, so it looks like the hardware is functioning properly. Any idea what could be going wrong here?

I decided to abandon developing this through Game Center and to use Multipeer Connectivity instead.