Those are really cute! (I missed it the first time around.)
You did great with the double sided registration, but there might be an easier way to do it…tutorial here:
Centering the designs around the vertical center axis is critical, but the addition of a weeding cut around unusual shapes makes it easy to do the engraving on both sides before cutting out the shape.
(I did that with the two sided carousel horses, and they are a very irregular shape.) But do a small weeding rectangle around each cut, don’t try to flip the whole batch over at once. That would be hard to align well.
Alternatively, especially for arms and legs, put two copies of the design side by side, but flip one. Then for the next pass, you switch the two out and just engrave the same pattern as it is already set up.