How should I install an access panel in a high traffic floor?
The thin flooring poses a problem. If it is too thin to have enough body of its own to be handled as a removable 13x19 inch piece, I would probably try to use the trapdoor as the base and glue a slightly oversized (by 1/4 inch all sides) piece of laminate to the door. Trim the rest of the flooring so it abuts the edges of this oversized piece.

If sealing against moisture is necessary, I would bevel the outside edge of the trapdoor opening and glue in some soft foam insulation bead that sits just barely above wood level. Laminate overhang presses down on that.

I would also probably put a removable saddle on the seam in the doorway. It could be held down with two or three removable screw.  It would protect that joint line and give you something more substantial to handle and seal, at least on that edge.

Finally, I would insert a lift ring somewhere through the laminate and into the trapdoor for ease in removal: