Are you using the fan speed adjustment on ATI Tray Tool correctly? Are you setting it up to be dynamic, based on temp... or just telling it to stay at 100% all the time? If you set it up dynamic, it will kick in when the GPU reaches x#C and then it will drop back down to whatever % you told it for the setting below. To make sure your fan can stay on 100%, click the option to keep it at 100% all the time. Obviously, that's loud and you likely won't want to keep it that way... I just want to rule out a faulty fan before we move on to other ideas.
My XTX is set up so that the fan stays at 27% until the temp reaches 70C, when it kicks up to 50%. That happens in my house fairly often (summer comes early in Texas). I can't really hear the fan go from 27% to 50%. Then, the next step for mine is at 80C I think where it goes to 100%. I can hear it kick in to that when gaming unless I'm wearing my cans. It usually goes in and out from 100% every few minutes as the temp ranges from 78C to 83C while gaming. I might set up a profile to just keep it at a full 100% while gaming so I don't hear the wind up/down.