If you are in the airspace in the continental US, on an IFR flight plan, at 10,000 feet, then you are in controlled airspace.
No, that would be the Eastern United States, where a man getting up to shave in the morning qualifies as the tallest obstacle in a thousand mile radius.
Again, you are wrong. First, you tell us that navaid service volumes apply to uncontrolled airspace, when they do not...particularly in light of the book you quoted (The Air Traffic Controller's Handbook) applies to controlled airspace.
Next, you make the assumption that all airspace above 10,000' is controlled airspace, when in fact, it is not.
One more strike, and you're out of here.
That will be a dozen hail mary's and you'll be needing to butcher a small animal and toss it on the barbeque as pennance.
Doesn't do a whole lot for the animal, mind you...but who said life is fair?