I like VHB tape, but not sure about it for these slats. Maybe you all are getting one of the less common sizes (?), but the usual stuff I get has 1.1mm of foam backing. Maybe you can order it with less, but that's what I typically see in your basic 4941/5952, etc.
I wonder if that would trap dust and stuff along the upper edge (where you already have a slat edge, plus now foam and perhaps a tich of adhesive).
It also seems like it would be a bit of a bear to get it all perfectly placed (keeping in mind the OP will have highly contrasting white "stripes" between each slat). And then you have to apply X amount of pressure to help the tape set. Can the plywood backing accept this pressure (not sure how it's attached or how thick it is)? Will the slats "creep" out of position?
I'm not saying it can't work; more just sharing the thoughts I would be having if I were considering it as an option.
Personally, I'd use screws, perhaps making some sort of layout stick for the holes/slats. I guess with the white stripes, I'd be thinking some day I'm going to need to repaint those, or some other inevitable boat maintenance chore that would involve removal.