AirPlay only works over wifi or an eithernet connection which means you would need the wifi password for every courtroom you work in. If a courtroom doesn't have wifi, will not give you the password or happens to go down before or during your presentation you my friend would be screwed.*
My recommendation would be to use an Apple TV, iPad 2 and a Seagate Goflex Satellite Hard Drive. The Goflex Satallite broadcasts its own wifi signal, the battery lasts from 4 - 8 hours depending on use and you can mirror your iPad screen to your Apple TV over the wifi signal (also play videos, music and documents). This would be the best option that I can think of at the moment. I just tested all the above on my TV and it works great. I have a bulb on order for my Acer P5270 projector, I'll post the results from that once I get it up and running (hopefully within a week) but I expect it to work fine. The only other issue I can think of is sound. My projector doesn't have a audio out plug and most speakers are horrible on projectors. The Optima PR160s would probably work fine. It has HDMI in and stereo audio out so a cheap set of computer speakers might work depending how large the room is.*
It might be a slightly over your budget (Optima projector $479, Goflex Satallite $200) if you already have an iPad. If you go with a setup like this it might be best to get a custom pelican case to keep the equipment safe and look more presentable when entering the court room.*
Hope this helps,
Brent