Well, I got rid of the 410 error by using the 1.1 API:
SLRequest *postRequest = [SLRequest requestForServiceType:SLServiceTypeTwitter requestMethod:SLRequestMethodPOST URL:[NSURL URLWithString:@"https://api.twitter.com/1.1/friendships/create.json"] parameters:tempDict];
Now I get a 400 error:
HTTP response status: 400 Error 0error (null)
Which suggested invalid authentication, even though the code above looks exactly like the code I see on every tutorial/example I find. I guess I'll create another question...