If a route loops around over a great distance, as is usually the case, I think basing the signage on the dominant direction in that part of the road makes more sense than basing it on the overall direction of the entire road. This is because you can't have, using this road as the example, US-101N/S suddenly turning into US-101S/N. There will be a substantial stretch where it switches to US-101E/W between the two. So while driving in any particular area, the suffixes will be meaningful to any driver with a reasonable sense of direction and understanding of the geography, and not confusing in any way.
A 360-degree beltway could use N/S for roughly one quarter, then E/W for the next quarter clockwise, then S/N for the next quarter, and W/E for the next one.
Cape Cod could switch US-6 from E/W to N/S at the Orleans circle, and then W/E in Provincetown.
I notice that CA-18 and CA-38 in the San Bernardino Mountains have dramatic doubling back. Both or basically horizontal through most of their lengths, but a line connecting the ends of CA-38 is closer to vertical. California solves that by simply not putting directions or direction suffixes on any of the signs.
Yes, CA-18 is probably the strangest route in California. Only the straight portions out in the desert (west of 15) will be consistently signed. The rest just isn't. Though there's no reason it couldn't just do what 101 around the peninsula does, and just have direction banners that are relevant only to that portion. CA-18 did make a bit more sense originally, though, when it actually started in the LA area (thus its number). It had more west-east alignment that fit something of a grid. Only then did it turn northeast and go through the mountains.
The biggest problem with CA 18 is that the segment west of Victorville should have just been designated a totally separate highway.
When I dabble with theoretical renumbering, that's what I always do. Perfect 138 extension if that route didn't turn southeast instead. But I suspect 18 might be extended west of Victorville so that it begins at 138, as 138 later ends at 18. Creating sort of a mini-loop.