In 1990 I ran Golden Spike in a stock, "open" FJ40 with 31 inch tires. The only obstacle I didn't make it over on my own was the Golden Crack.
That being said, I've run 33's on my last FJ40, the pale yellow one I wish I'd never gotten rid of, and my FJ55. I think you'll be happier with the extra clearance. You'll want 3 1/2-4 inches of suspension lift, but I think you'll be happy. I never had any problems with rubbing in my FJ40 and I ran stock back spaced wheels. By the time you air down those 31's in Moab and some of the places we run here, you'll have very little ground clearance. Many people run 35's or larger and think anything smaller is too little. The 40 I'm building will have 35" SSRs which is the largest tire I've ever run. The problem with tires much larger than 33's is you start breaking things more easily.
So I'm encouraging you to go with 33's also.