there is, in my opinion, nothing inherently wrong with your session. 4 x 800m in 2:24 is, as you say, your mile pace, and a reasonably well conditioned runner should be capable of 3km - 4km of repeats at mile pace. the difficulty I'm having is understanding why you had a recovery as short as 2:00. this should have been around the same time as your run, around 2:25 - 2:30, and, depending on what you've been doing up to this point in your training, I might start you at a recovery nearer 2:40.
and, as for the "trick" you got from the Steve Magness website, it's approximately 50 years old, at least. David Hemery discussed it in his book after he won the 1968 olympic 400m hurdles. there is very little new in this game, everyone knows about the various ingredients, all we are really discussing is the recipe.
Yes, I might have been able to finish the workout without the 'trick' if I had taken longer recoveries.
There's nothing wrong with dusting off an old ingredient, is there?