I know I talked about it before, but my brother had the same issue with his GS-A. Like the California model FJRs, he had a charcoal canister. If he would fill the bike and then let it sit on the side stand for a while, the bike would run like crap.
It happened a few times on local rides, but on the way to and from South Carolina earlier this year it happened a lot. Usually, we would get fuel, then take bathroom breaks or eat, so the full bike sat on the side stand.
He started Googling his problem and found that lots of GS-As had the same problem. It was caused by too much fuel venting into the canister due to heat and the side stand. If the canister got saturated, the bike would run like **** until the canister burned off.
He found instructions for a 'canisterectomy' and did the mod. After removing the charcoal canister, he hasn't had any problems.
There was a guy with a Cali FJR having the same issue a while back. I told him the same thing and he removed his canister a little bit later. If I remember right, that solved his problem too and was pretty easy.
FYI...