Yeah, foil or tape is fine, can even be aluminum foil on cardboard. As long as it all connects, and the shape and dimension are right.
Which, uh, impedance will depend some on the exact width, thickness, and dielectric constant, of the traces and substrate at the feedpoint. So that end should probably still be PCB. But the bulk of the element areas -- where not overlapping -- are basically in air, substrate doesn't matter out there.
I have a suspicion that having the antenna that close to ground does something with nearfield/farfield transition but I know very little about vivaldi antennas (would be interesting if the antenna was designed around the impedance of mud assuming its not the same as air's 377ohm)
Heh, the impedance will surely be lower down there. Quite a bit lower if actual mud... You'll get a fairly strong reflection off the air-soil interface, at least from a distance. Good question, how much near-field counts for here, it's less than a meter away in the picture. I don't remember what works for evanescent waves / coupling. Perhaps a shallower angle, perhaps something loaded (fill the bucket with sand?), perhaps something lower profile like a bowtie flat against the soil?
Tim