Instead of integrating ball-catching-bags, you may build an angular board along the long side of the Pool Billiard table, which is starting right under the holes of the play-field. The balls fall on the angular board and roll down. The pitch of the angular board should be as low as possible in order to make the balls roll slowly and to have an staging area as high as possible. The rolling noise can be reduced by covering the angular boards with thin carpet or textiles like felting for example. To take out the balls easily from the staging area (central position where the balls roll to), saw an hole out of the short side covering board at the appropriate position. Don't make the hole too low if you don't want the balls to fall out automatically.