Will the screen stick on reassembly? Should I improve adhesive?

Since the screen has been infused with the LCD, you will not have the opportunity of cleaning it inside or between LCD and glass panel. So the job is over. No more dust worries!

Regarding any upgrade that is intended, you will surely need to secure the proper adhesive stripes before opening it. Once you pry-up the glass from the frame, and the adhesive comes out to the air contact at various temperatures rather than intended, it gets weak and won't seat as seamless as was before. I would not suggest to tear it down without having required adhesive stripes in stock.

Seems like Apple's guiding us to adopt and follow the shiner road that is seemingly narrow and delicate. A simple miss-step would come to be a devastating move.