There's no issues with the timeline as such if you just move it a couple of years. Pathfinder 2nd ed assumes the AP happened at a certain time, but that doesn't seem to matter much either, as long as you keep it in mind for future APs that might touch the region.
However, you will need to explain why Cheliax - as soon as the queen learns the PCs murdered her appointed Lord Mayor (and her cousin to boot) - does not just send the fleet to Kintargo (assuming the PCs stopped the Menador route) and just level the place. Like they did to Pezzack.
If you don't plan to play further than book four that won't be as much of a problem, since Barzillai has reasons to play things close to the vest and might whitewash the goings-on in his duchy to the queen. But after he's killed there's no reason for Abrogail II to not stomp down hard and crush the rebellion before it spreads even further. In the AP she can't, because when Barzillai is offed a major city close to her capital is occupied by paladins and even nastier critters (nasty from a Thrune perspective, that is).
In the same vein, if you don't use the looming threat of Chelish retribution and regaining of control, there's no incentive for the players to deal with the Kintargo contract and most of book five. You would then have to skip book most of five and go directly into book six.
Or you could invent another national crisis on the same level as the Glorious Reclamation to explain why Cheliax doesn't hit back and give a sense of urgency and momentum. But that seems like extra work for no benefit since there's already a reason given in the AP.