Ahhh you’re trying to align to the slats - both vertically and horizontally. And I’m guessing the slats aren’t all the same size (or maybe that’s just distortion from the picture)? So probably moving each piece of text manually so that it appears aligned?
That doesn’t sound like fun to me. 
The camera is really going to be for general alignment, at this point… not precision.
However, your center alignment (Leah, Brian & Emma) looks pretty good. The rest of it is off as you get further away from the lid camera. And I guess you have the crumbtray out, making actual material height even more critical.
It looks like you are able to engrave it all in one go though, without moving the material.
And your center alignment is pretty good on the Leah, Brian & Emma.
I’d set up a document in AI that mimics the piece you’re working on… you could do it a couple of different ways, a rectangle for each slat (if they are different) or, measure the outside dimensions of the whole piece and then measure the height of the slat and put a guide for each one. Then, you can align your text off of the individual rectangles or the guides (whichever method).
Once you get it in the UI, adjust everything together, since it’s aligned in the design. Since your center alignment looks to be really good, align the Leah, Brian & Emma line to where it needs to be and the rest should fall into place if you measured and put things correctly in the design.