Gas pumps shut off prematurely

"Any 'flappers' in the filler neck our FJ's that could stick or partially open?"

No, there isn't (its a straight shot of about a 1" diameter tube all of the way to the inside of the tank).

There is a check valve in the vent in the top of the tank, though. When the nozzle is pressed all of the way into the filler neck then air / vapor in the tank that gets pushed out as the tank is filled is directed through the charcoal canister, via that vent. That air/vapor, after it has passed through the charcoal canister then exits the vehicle through the little air filter on the end of the 1/2" diameter hose that goes from the charcoal canister to it.

The check valve's job is to protect the charcoal canister from being ruined if raw fuel were to reach it (the check valve prevents liquid fuel passing, only vapor).

If there was a fault in the check valve it could cause an issue, but would require replacing the entire tank to find out.
If there was a fault in the charcoal canister it would likely throw a code (it does periodic self tests).
Most likely your air filter is clogged with silt/dirt. I wonder if cleaning that out would help with your filling issue?

In the photo below, of the area below the rear cargo area, the charcoal canister is the rectangular black box to the right, the air filter is the thing attached to the body beside it (middle of the photo). There's an air hose going from it, to the right, to the charcoal canister, and one going up, to the left, to a snorkel mounted near the top of the filler neck.

Scotty described doing about the same thing I was talking about, but he was using an early '00 vehicle with the far simpler system fitted to US vehicles prior to about '06.

On the FJ, the 1/2" hose I described is the air exhaust/intake, and the hose from it, to the canister, then to the tank would be the rest of it.

Check that filter first, and its hose on either end, then if that is not clogged with dirt (or creature intrusion) then proceed to inspect the canister.

In his example the evap canister is a pretty cheap cylinder with activated charcoal (aquarium filter) in it.
The one on our FJs is far more complicated, with servo controlled valves and a small air pump and some other stuff which makes it very expensive to replace (hundreds of $). So, definitely make sure it is not something simple like a dirty filter first.

The good thing is, if it is just dirt/creature in the air line, then other than having to get under the rear of the vehicle it should be about as easy to clear as what he was showing in his video of an old car.

Norm