Using ArmorAll was your first mistake.
I use a feather duster to clean dust off my instrument panel. It doesn't scratch. I think I started a thread about this and some others had good alternatives.
Regarding the hazing. there are some plastic polishers available. I guess I would try water first, then water and vinager, then maybe go for the polisher.
Most vinyl cleaners make a haze on glass, but glass cleaner removes that. Just don't know about the plastic. Start mild, then work up.
Good luck.