Thanks for the question! So the labels only depend on the limits of the plotting window, which you can supply as a keyword option. In that sense, and together with using the same gridlines options, you could have the same background in some sense.
What uniplot cannot do today is to have multiple vertical axis (like weight and head circumference in your example).
Hope this helps!
P.S.: Regarding your PDF question, for that in fact I think that some plotting library to graphics (rather than the terminal) might be better