The clay you're displacing has to go somewhere. It moves everything out of kilter. The only way I see that working is if you made a jig to hold the dowels spaced an appropriate distance apart and press the clay onto it. Even then, there's no way to make the clay the same height all over.
Also, you'd be making blind-end holes. Often I put the mouthpiece and condom on when they're still in the tray while I'm waiting for the filled-with-excess-from-first-ones are soaking in. When I'm done, I can lift the whole tray up and have them standing there ready to be stacked.
Oh ok, I see how you got it.