Hi Nick,
Test Day is a rather specific 'event' - the details are specific and they matter, so you have to train as best as you can for all of them. The more realistic you can make your CATs, the more likely the score results are to be accurate. The more you deviate, the more "inflated" your practice scores can become - and that's what happened here. By taking the CATs at home, taking them at different times of day, taking longer breaks, etc., you weren't properly training for the FULL GMAT 'experience.'
Test Day involves a variety of really specific steps and parameters (including steps before the Test even begins - such as leaving your home, traveling, etc.). Every factor matters, including the psychological ones, so you have to put the necessary effort into making sure that you take your CATs in a way that 'matches up' with as many aspects of Test Day as possible. If you don't do that, then we won't have a clear idea of how well you might perform on Test Day.
In addition, it's possible that you were trying to do too much during the last few days before your Official Exam. If you were working a lot and studying during those last 3 days, then you might have been too tired to perform at your best. It's also not clear whether you took the GMAT on Friday or Saturday - but in either case, that would be at the 'end' of the work week, when you would likely not have been at your best. Most Test Takers actually perform at their best on a Monday morning (after they've had the prior weekend to rest a bit and do a little light studying).
Thankfully, those are relatively easy issues to fix - and now that you've taken the Official GMAT, you know the EXACT details of what happens on Test Day, so you can better train to mimic those details during your CATs. That having been said, to raise this 420 to a 580+ though, you're going to have to make significant improvements to how you handle BOTH the Quant and Verbal sections - and all of that work will likely take at least another 2-3 months of consistent, guided study.
GMAT assassins aren't born, they're made,
Rich