Using the syntax @rog suggested in his comment, I was able to adapt the code from the second link in my question (concerning downloading) to allow for basic authentication, and completely eliminate the need to subclass AFHTTPClient all together. Here's the (redacted) code I used:
NSURLRequest *request = [NSURLRequest requestWithURL:[NSURL URLWithString:@"ftp://myUsername:myPassword@www.mysite.net/myfile.sqlite"]];
AFHTTPRequestOperation *operation = [[AFHTTPRequestOperation alloc] initWithRequest:request];
NSURL *path = [[[app applicationDocumentsDirectory] URLByAppendingPathComponent:@"myfile"] URLByAppendingPathExtension:@"sqlite"];
operation.outputStream = [NSOutputStream outputStreamWithURL:path append:NO];
[operation setCompletionBlockWithSuccess:^(AFHTTPRequestOperation *operation, id responseObject)
{
NSLog(@"Successfully downloaded file to path: %@",path);
}
failure:^(AFHTTPRequestOperation *operation, NSError *error)
{
NSLog(@"Error in AFHTTPRequestOperation in clickedButtonAtIndex on FlightInfoController.m");
NSLog(@"%@",error.description);
}];
[operation start];
This doesn't actually get me any closer to knowing why using the [[AFNetworkingHelper sharedManager] setUsername:@"myUsername" andPassword@"myPassword"];
failed, but on the plus side I'm getting the behavior I want from my app. I guess I can live with just that.