Couple of things to watch..
Firstly, inflatable structures outdoors have another name, a "sail". Inflatable screens have this problem in spades, and usually require significant (as in tonnes) of ballast to be safe (And even then there are upper windspeed limits that require the area to be cleared if they are hit). Scaffolding carrying a screen frame and a proper perforated projection surface is actually easier in some cases.
Secondly, projection has this nasty little gotcha in that the area rises as the square of the screen dimensions, 5000 lumens is ok on a 4m (16 square meters) screen is subdued light, but an 8m (64 square meters) one needs not 10,000 but nearer 20K lumens and that is a LOT of money in video projector. Of course you could go for old school film gear, there is a lot of it kicking around right now, an FP4 or even an old Ross or Westrex in a portacabin with a cakestand and a few KW of xenon lamp would get the job done, but then you need somebody who knows what they are doing with film as opposed to video.
Thirdly, Copyright... DVDs are licensed for private performance only, public presentation usually works on a percentage of the gross subject to a minimum guarantee, rights are an issue here (And the Mouse is really hot on this shit).
Fourth, Cardboard? 'Hello Mr fire marshal please shut me down right now'.
3,000 people in a field is also a major logistics headache, everything from toilets to medical cover, to drinking water......
I would be looking to hire this done, especially if you are only running three events a year, it takes care of all your technical and much of your liability risk, there are folks who will set up a drive in movie in a field.
I am not trying to pour cold water on your thing, but do give the logistics serious thought, do talk to the licensing folks and do run the maths on it.
Regards, Dan.