Enwisage this, as Mr Chekov might say...

Get one of those cheapy pressed/rolled steel curtain rails, the ones shaped like |________| that are expand to fit... stick either big magnets or suckers on the ends, so it can attach to your car at the top of the windshield (On the outside!) Then get a black shower curtain or something similar, that bunches up tight along the rail, put magnets in the side to hold on the A pillars, and magnets in the bottom to pull it over top of the vents... depending on angle and rake of your windshield you might need another in the middle... Can probably hack it up for $5

Could even epoxy the fittings for the curtain rod to the A pillars, they're fairly low profile... and if you want to get fancy velcro the sides instead of magnets... Might need more bend in the rod if you've got a curvy screen.... Inside the car you might wanna put up a normal sunshield to help keep out long wave IR from it that would warm the car up more.

Commercial rights reserved :p (In case the "car bra" makers or anyone wanna produce it)