If you're able to afford the $50 that hand scoring costs without a problem, then you might as well order hand scoring for your June ACT essay. If there is no change or the change isn't in your favor, you'll have paid $50 for the confirmation that perhaps you had some issues with ideas and analysis on this particular test (which could give you a better idea of what to work on for the next test), and your scores will stay the same; if there is a change in your favor, ACT, Inc. will change your official score report (and you'll get refunded the $50). As you can see from some of the comments on our article about problems with ACT Writing scoring, several students have ordered handscoring and seen huge (3, 9, and 10 point) increases in their Writing scores. Since ACT, Inc will only change the score if the change is positive, this is a strong incentive to order hand-scoring.
If the $50 is an issue, though, I'd recommend against ordering hand-scoring, because the fee will only be refunded if the score is changed in your favor, and the difference from your December subscores to your June subscores isn't unreasonably large.
Unfortunately, there's not anything you can do about your December ACT Writing score now, as it's been more than 3 months since the test date. Fortunately, with the change to the ACT Essay scoring, schools may end up converting your old ACT Writing score to the new, out-of-12 ACT Writing score (which is just the average of your domain scores); for you, this means that your December ACT Writing score will average out to a 10/12, while your June ACT Writing score will average out to an 8/12.