@MS...Some thoughts...
“extending even above the electrolyte. “
Might be due to splashing up of electrolyte…
“The Ni wire is now black,”
Some possibilities (from C&W again, pps 890-3):
NiO is a green solid, but on a wire surface could look black. Forms when hydroxide (deuteroxide) is heated (the description might be for solution, but should apply to solid surface also I would guess). (Also recall that long time at low heat can often slowly do what happens faster at higher T.) Ni hydroxide would form on the surface by reaction with LiOH(D). NiO dissolves readily in acids, so you might try a quick dip in some acid and rinse to see if that removes the color once you are done.
NiS is a black solid. I would worry that perhaps you are extracting (leaching) some sulfide from the paper cover. That would take a little time to build up enough S(2-) in solution, so the timing of the black color’s appearance might negate this possibility (if it happened very early in the run (Sorry I don’t recall the details of your run). You can get S from the air but I don’t know if you could get enough to do what you see. Lots of acid rain where you are?
Notice that these are not electrochemical reactions I am talking about, just normal ‘solution’ chemistry. Doesn’t mean there aren’t electrochemical reactions too though…
Edit: Found an interesting paper on determining reducible sulfur in paper. Very low concentrations found usually. Note comments on 'tarnishing', which is blackening of course: http://www.tappi.org/content/tag/sarg/t406.pdf