We have a hard keeper as well. We feed him a full scoop of beet pulp(soaked) and a full scoop of low protein sweet feed. We also give it to our other horses. They only get this four times a week. He has put on the weight that he needs just fine. They don't seem to get antsy either.
If your horse is in with other horses, there may be another horse that is keeping yours away from the free choice hay. So he wouldn't get to eat when outside. Spend some time one day and watch your horse to see if that is happening. If that's the case, discuss with the barn manager what options are available, like a second bale, or putting him in another pen.