For posterity:

I solved my own problem in an unconventional way. I didn't find this method anywhere online, but it works for me.

I need to be able to reference the ViewController object (the thing that handles the user interface and the controls I put on the user interface) after it's already been automatically created at program startup. Supposedly this is the "right" way to do it, by accessing the main storyboard by its named identifier, but that wouldn't compile in my project, with various parts of that example code refusing to even compile. Keywords like "UIStoryboard" and "instantiateViewControllerWithIdentifier" are simply not recognized by the Xcode compiler at all, saying that they are undeclared identifiers. I don't know why this is the case because every example on the web says "this is the way to do it". I can only imagine that these examples are all from old versions of Swift/Xcode and there is some kind of a new paradigm that I'm not finding in my Google searches.

Since for this particular application, I don't need to be creating and deleting windows, views or storyboards (it's mainly got a single UI window that never changes except for some text output to a logging window), I was able to turn the ViewController into a weird sort of a Singleton and reference it that way. Though there are examples of singletons on the web, I haven't seen an example of making a ViewController singleton, but after some poking at it, I suceeded in doing it. I did it like this:

In the ViewController, at the class level, create a variable named "sharedInstance". Examples of doing something like this for singletons exists on the web already, but I had to do it a special way, starting off with the variable set to nil, and also using the Optional indicator (the question mark), because it wouldn't compile unless I put it there.
Code:
    static var sharedInstance: ViewController? = nil


Then, inside the "viewDidLoad()" function that was already there in the ViewController, I set the variable for sharedInstance to "self". I had to do this after the view loaded so that it references an actual instance of the currently-running already-initialized ViewController.
Code:
    override public func viewDidLoad()
    {
        super.viewDidLoad()

        ViewController.sharedInstance = self
    }


Now I am finally able to reference the ViewController and its control outlets from any module in the program by referring to it the same way you'd refer to any singleton, with the added trick that I also needed to put the Optional indicator (the question mark) here too:
Code:
            // Log some text to the Text Field control on the main storyboard:
            ViewController.sharedInstance?.TextField.textStorage?.append(NSAttributedString(string: "Hello World!\r\n"))
_________________________
Tony Fabris