My first thought is you really need to screw it down but not to the existing roof. I would cut wood spacers to fit the gap between the exterior roof and interior ceiling and side to side. Make them a 1/16 or an 1/8 undersized up and down which will help pull every thing tight later. Screw the aluminum you have to the spaces and trim out a piece of 3/8 or so ply and screw that to the spaces from the bottom. This is where undersizing will pull the two covers tight. Use Proflex Sealant under the aluminum and any exposed hardware on the roof. Seal the edges of the aluminum plate Eternabond. Also paint the aluminum before installing.
To make the interior cover look a bit better you can add edge wood to hide the ply layers. Give it a coat of paint to match the interior ceiling color. You could also fill the space between the upper and lower covers with spray foam or fiberglass which will help with heating and cooling plus deaden sound.
