I guess I don't really understand the layout. I don't see any buckets, just the square tubes. Unless the round spots where the square tubes are, are supposed to be the buckets. Then I'm confused as to how you plan to put both in the same space. Also I would never fit through a 1.53 or 1.72 foot pathway, unless I stood straight up and walked sideways. Even then I simply wouldn't have any room to maneuver. And that's even without plant foliage invading the pathway that needs to be maneuvered around as well.
Also, if I understand correctly the plants in the tubes are planed to be spaced about one foot apart in each tube. I know choosing varieties makes a difference, but I'm simply not familiar with any varietals of squash, tomatoes, cucumber, peppers, or eggplant that don't get more than one foot wide. But at the same time the 5 inch tubes look to be touching each other, that would make the plant spacing just inches apart, even being offset from the tube next to it.
Then I see 8 foot long tubes, but less than a 3 foot long space to pull/slide them out with, So I'm not sure how that's supposed to work, unless you plan to harvest/pull all the plants at the same time. But then that eliminates the ability to rotate plants as they grow to maximize space/yields. Another concern (but again I don't think I really understand the layout) is how closely spaced the plants are. Not only because there dosen't look to be enough room for the foliage, but the inner plants are likely to be blocked from light because of the foliage from the plants closer to the greenhouse walls.
P.S.
Just a side note, I would cut the sponge material for sprouting the
seeds into cubes first. That way you don't damage the roots later.