I would argue three points would, in general, be worth the wait-thinking in terms of better school choice, higher chance of admission to targets, scholarship money, etc. This of course might depend on how long LSAC takes--several months would probably change the calculation. That said, you won't be applying early at this point anyway, so I don't see how a few weeks would hurt.
By the way, when you say you hand scored it yourself, do you just meant that you looked at the pdf of the answer sheet on Lsac? If so, you might check with someone less biased in your favor just to be sure your judgment is sound. Applying later with no boost would be the worst of both worlds.