I actually think your third option is right, not a cop-out. There's no use deciding to use a cleaner now, only to find out that everything came off with the wash.
After you wash, if you still have noticeable spots, I'd hit it with the
AIO, personally. I don't see why that would make your top layer any less durable, as long as you put a complete coat of protectant on (always a good idea to do 2 final coats in case you missed any spots).
John