OK, the results are in, and zinc doesn't help cells take up DNA. Here's the data:
Adding zinc doesn't increase transformation frequency (the simplest and most sensitive measure of DNA uptake). The small differences between most these columns aren't significant, given the modest scale of this experiment. High concentrations of zinc are probably a bit toxic: at 1mM zinc decreased transformation more than 2-fold, and at 3mM it decreased cell viability 2-fold. (I missed adding the DNA to the 3mM tube so I don't have this transformation frequency.) Adding the zinc chelator histidine didn't decrease DNA uptake either.
The conclusion: we can probably rule out an important role for zinc or zinc-finger proteins in DNA uptake. Is this an important enough experiment that I should do it over several times, to get data with good error bars? It's an important experiment, but if the possible effect of zinc is too small to have shown up in this experiment it's probably too small to be interesting.