I’m not certain what “Lincoln narrative” you’re referring to but as far as I can see it must be the Lost Cause “Lincoln narrative”.
From day one (or even before!) Lincoln expressed a deep desire to work with the disaffected south. The oft-quoted “My paramount object in this struggle is to save the Union, and is not either to save or to destroy slavery. If I could save the Union without freeing any slave I would do it, and if I could save it by freeing all the slaves I would do it; and if I could save it by freeing some and leaving others alone I would also do that.” the Lost Causers mistakenly believe to show an ambivalence on slavery really showed his primary intent - the protection of our nation. Yes he wished to eventually abolish slavery but he demonstrated a willingness to postpone and slow-track the process in order to accommodate a people who didn’t want to be accommodated.
Lincoln’s proposed legislation hit on all cylinders. It would have prohibited the repellent Particular Institution within DC; it would have outlined a positive process towards emancipation for the affected; and it respected the existing slave-holders outside of the jurisdiction. I can see why the southern fire-eaters, who had zero desire to work towards a peaceful resolution blocked it.
I don’t know if you were trying to be deliberately disingenuous about a non-existent Lincoln “fugitive slave act” but IMO you definitely missed the mark on this one.
At the risk of repeating myself, Lincoln’s bill required municipal authorities to provide the means to arrest and return fugitive slaves to their owners.
To paraphrase Shakespeare’s famous line about a rose, a fugitive slave law by any other name still smells like a fugitive slave law.