I warning everyone that this will turn into another one of my long posts!!! This is a writing and project in progress.

Seeing your picture is a good idea, that is, except for the tape or what looks like tape. Did you paint all of that in place to match as it still looks good!

Anyway, I stll respect the use of tape as for the last two years I have been sticking, "Glad Press and Seal" to literally cover the vents closed shut. The stuff does not stick that well and is not reuseable but is cheap.

I only used this setup, when I visit my sister-in-laws house in Southern California, because she has a large (protected) California Oak tree in front of her house. Next month, I will be down there, again!

I like the shade of the tree but not those darn leaves. The leaves fall all year-round. They are small, curly and dry out quickly. They then turn into crumbs or end up whole in the rocker panels. If I park anywhere else, the sun bakes the car and especially, if you seal up the vents.

Here is the ironic part, I was in the process of making some solid vinyl sheet covers from a panel of left over shower surround material when I spotted the thread and your post. I had just made a paper template so I could mirror image for cutting material into parts too!

During this earlier process I was still rolling around the idea of an easy on easy off method and how these were going to store when not in use. Also, I needed to have them held in place, just in case, I or my wife forgets to remove them before driving away.
I was thinking of using some stick on-foam rubber sealing tape on the flat solid vinyl panels but the thickness was an issue that was butting up against another one of my design perimeters I defined early on.

Here is where your screen idea crept into my thoughts along with the rubber idea as a hold down component.

I see how your lays on top and is about the same thickness as my vinyl but has holes. I do not know what you used but it looks like gutter cover material. My material has no holes and the thought of adding them seemed like even more trouble.

Here is where I think I will try to use another rubber idea. I think I will narrow the ends about a half-inch from both sides over the end louvre slots.

My plan is to use rubber hose that fits the width and lengths of those end slots. Vacuum hose or windshield washer hose fits nicely at the moment.
I plan to slit the hose through both sides across from each other and about that half-inch from the ends of the hose and thread the screen through the hose sides.

After fitting the two hoses with the screen, partially down into the slots, to set the length adjustment correctly I will lock the screen to the hoses.

I will do this by using silicone door and window caulking. I have some of that fifty years stuff laying around all the time. I shall pump the hose full from one end until it comes out the other end or shoot it in from each end.
This should dry and still be flexible and squishy. I may not fill them up completely, I just want it to lock the screen to the hose.

Seeing how it all works will be the "on the fly" part of my prototype.
I am still curious how the edges of the cut window screen material will behave, but then, they are for temporary use!

The other idea I have visualized about this design is that they will roll up when traveling and stay in a cars tool bag!

Now looking at your screens, that match so nicely. You could use the same rubber hose idea to remove the tape that may give up the ghost later, as tape usually does.

You could add the rubber hose on the bottom sides of you screen material.
Have them held to that screen with short, small diameter screws through on side of the hose. Can I suggest using short lengths of rubber, maybe an inch or less, dispersed equally for that flat down fit, you have now on the cowling.

Thanks for your picture, as it sure cut down on my reading of your post, to understand what you did!

Phil