ArcherB,
The tomato roots will pass through the sheet like a hot knife through butter.
While the sheet will minimize your Potting Mix from dropping down into the water reservoir, it will not prevent the roots from getting down into the reservoir very quickly.
This is what you are going to end up with:
And you may have now created another problem of too much wicking as the Landscape Fabric, while being water permeable, does not wick water as your cloth sheet will. In essence, you've created a 14 inch by 26 inch wick along the entire bottom of the Aeration Bench.
Can you un-do this and use the material I recommended?? I put a lot of thought and "science" into the design and use of the EarthTainer which the cloth sheet violates.
Raybo