You raise some valid points and establish some plausible doubt, and I don't want to get any further off on GRRM thread in a Butcher thread. To save time, I'll acknowledge your Prologue reasoning is pretty sound about him not wanting to return to the wall period, which justifies the run, though the believability thing is not convincing. He might not be the savviest person in the world and thus might not have thought to say "I think it was the others, but it could have been wildling pretending to be, I saw them with my own eyes but those can't always be trusted" which is what everyone would have thought anyway, A) He's lying to cover his/their failure, B) He's telling the truth, C) He's wrong but believes it, superstitious peasant and scared, or D) He killed them. A & C are the ones the leadership at the wall is going to default too and he would know that. But as you say, getting away from the wall is reason enough.

I wasn't particularly convinced with your Cat or Stannis reasoning, fans can almost always construct a plausible excuse for author's taking a route that seems unnecessarily complex or flawed, arguing the matter with you isn't likely to achieve anything, particularly since it was pretty plausible.

R+L=J, I don't see that it effects my reasoning, unsurprising since that I thought that as an option was pretty strongly implied. After all if she were just his non-pregnant and unwilling rape victim it is hard to imagine Dayne and co keeping her there against her will with the Prince and King dead. It is at least in the realm of plausibility that the Kingsguard might have reasoned Ned would want the child dead as a Dragon and unwelcome nephew, even believing Lyanna might be wrong if she said "No, he's my brother, he'd never do that." otherwise, without a kid, the scenario goes beyond WTF into absurd.

The suicide by Ned option is one I'd considered but not with the honorbound-to-tell-Robert aspect. Fleeing to exile with Viserys and co is still reasonable but then they might have been afraid to transport her pregnant and might have not been given that option by Ned on his arrival, though an offer of re-joining the enemy gives a better excuse for going it with only close friends. Ned had no reason to bring a less-than-overwhelming force if "Join or die" was the only options being offered. It really comes up short on inspection since Ned should have expected a real garrison and acted accordingly and been right in that expectation, but perhaps he brought a decent army with him and they specifically asked to meet him in a visually secluded place, though and arranged parlay wouldn't likely have been 3:7.

Whichever, I find your reasoning solid if not entirely convincing and I don't want to tangent off Butcher anymore and this could go on for pages, so probably best to call it quits here.