I had the hood of my '02 Highlander repainted due to stone chips. When I asked how long I should wait before waxing it, I was advised not to use a polish but a 'paint glaze'. Polishes were harder on clear coat finishes then glazes. I'm no expert on the subject but I would check any cleaning product to make sure that it states that it is safe for Clear Coat finishes.
I have been using Meguiar's Mirror Glaze on the '02 and now on my '06 Highlander and have been very pleased with it. It also does not dry white. I'll check out the Turtle Wax ICE next time I'm out and about! Enjoy the FJ. I am also interested in that model or a 4Runner for my next vehicle.