i see theon's arc in acok as a very strong parallel to ned's arc in agot and i've said before that theon digging his heels in at winterfell is a wolfbrained greenlander thing to do but it specifically mirrors ned's own strategy when he's in king's landing
the parallel is in their decision making style and in their total refusal of outside help
in agot, ned is offered an "out" from his position as hand in king's landing that would keep him and his daughters safe by like, everyone. varys, littlefinger, and renly tell him to get out before robert dies because they know exactly how this is going to end for him and his young girls. but it's not the honorable thing to do and he is duty bound to stay and reveal the truth of joffrey's parentage. so he stays and he does the "right" thing and he gets his head cut off.
in acok, theon captures a mostly-empty winterfell with thirty men and understands very quickly that there is no way he can hold this castle. with bran and rickon "dead" he doesn't even have anything that can guarantee his safety when ser rodrik returns (he ends up using beth but he knows this isn't a strong play, it's a desperate one). asha tells him this (after he already knows it to be true) and tells him to come back with her to deepwood motte, but he refuses. ser rodrik tells him to face the noose with honor and spare his men, maester luwin tells him multiple times that he cannot hold the castle and must surrender before he suggests for him to take the black, and he turns every offer down.
ned's decision to follow the same mystery that jon arryn was investigating and then his commitment to reveal joffrey's parentage is a course that everyone around him (who already knows the secret and has known the whole time) know will lead to his death. and they all try to get him to leave but he won't, because that's not the honorable thing to do. theon decides that the only way he can prove himself to balon and get his own justice for his ten years of captivity is to take and hold winterfell and be its rightful prince. that's the only thing that's fair and if he gives up after taking the castle that'll ruin what he's conceived of as justice.
in both cases, their death lurks at their elbow for the whole of the journey. for theon this is very literal, with "reek" tailing him around waiting to pounce, and for ned the danger is all around him and he refuses to see it. the "open secret" of joff's parentage among the castle's intelligence, the reality of robert baratheon and his horrible regime/inability + lack of desire to rule, etc. ned ignores far more omens (dead direwolf with a stag's antler through its neck) and red flags (being ordered to kill your daughter's puppydog) than theon does on his journey to the place of his demise (theon has a pretty successful run up until he takes winterfell) but it's a very. it's a very "that's his father's son" situation. to me.