^ I see a much greater priority getting I-587 switched to east-west than I-87, which is more of a 50/50 route given existing cardinal directions on US-64 and US-17.
Since most 3di's (with the exception of longer linear routes like CA's I-215, I-135, and I-476 generally don't have directionality attached, the easiest solution would to just not banner I-587. But if NCDOT insists on doing so, the argument for bannering E-W is bolstered by NY's rather long I-495, which
is bannered as east and west. IIRC, I-195 in RI/MA is as well. Since the chances of I-587 being fully signed before I-87 are pretty solid, applying a N-S orientation there is patently silly and likely confusing to the driving public; NCDOT should know better!
Alternative approach: redesignate it as a 2di like I-46; at 52-odd miles (not counting any extension over the Greenville bypass) it may be a bit short; but if folded back north to I-87 or south to I-42 there would be an additional 20 miles north or about 32 south. At that point any controversy over bannering would disappear.