Does LA have a requirement that you even have to have side windows in your vehicle? If not, roll them down and pull the fuse when you take it in for inspection and tell them the windows are broken. I do it every year in TX. If a cop tells me to roll them up, I'll tell him the same thing. It's not illegal to not have side windows in TX, so he can't force you to do it if you tell him the windows are broken and don't roll up.
That said, LA has always been stupid about window tint for some reason. TX is much more relaxed about it. Hell, we're in the south and it's freaking hot as hell here in the summer.