Call storyboard scene programmatically (without needing segue)?

Yes you can. Do something like this to get access to the VC, then just Modal Push it:

UIStoryboard *storyboard = [UIStoryboard storyboardWithName:@"MainStoryboard_iPhone" bundle:nil];
MyNewViewController *myVC = (MyNewViewController *)[storyboard instantiateViewControllerWithIdentifier:@"myViewCont"];