Without a false bottom i would pass on the air pump.
With the screen top you can also cut a small piece acrylic that fits over the screen area. You can then slide this back and forth to adjust the amount ventilation as needed.
Or i can get different lengths of plexi glass to cover some of the vent as needed
Plexglass warps and bends with heat, moisture and time. It's generally unsuitable not to mention expensive AND it scratches.
Glass, on the other hand, is cheaper, easy to obtain and fairly easy to get cut - LOWES, Home Depot ect...most glass stores. It doesnt scratch as easy, cleans and wipes off easier.
Use glass.....and yes....it should cover the whole / 100% of the top. The nessa air movement and circulation should come from you opening it up to feed and spray every day to every other day. The only time a fully enclosed tank is dangerous is when there is high heat - like 80F plus and when it's not opened regularly.