Anyone have an indoor fireplace at home with screens in the doors? Doors closed, some heat - doors open, inferno. Screens will cut back significantly on air flow, especially if it is gravity (refer). Best solution is to provide twice the amount of surface area of the screen. For example: let's say the one of the refer grill opening is 2'x3". That gives you .5 sq ft. Instead of a flat piece of screen, you need to build a box 24" long by 3" wide by 2" deep (+/-) to give you the surface area you need. Take a look at the covers for furnaces - they are domed shape to give the required surfaced area.
2015 Silverado 3500HD CC Long Bed Diesel
2016 Silverback 33IK