Apostolic Succession isn't that closely connected to the filioque.
In fact, filioque is one of those `possibly slam dunk' easier concessions, I have always felt in my own opinion, that Rome could make toward them where the East is concerned. If for no other reason than that Nicea said the `creed was not to be changed' the Easts objection to the change seems solid. Just don't change it. Yet they did. And not only that, but it went thru a period where Western Popes like Leo III were aware it was a reading that was starting to drift. The heart of the issue is it started not as a theological reality and meaning debate, but the equivalent of how something can get a bit mangled in vernacular. Yet very soon, as "investments" in positions built up on both sides, advocacy began to obscure this pattern.
Complicating the issue was an argument with Constantinople over jurisdiction and even some secular matters tha in the late 880's not long - in medieval terms at least - after the time of some of the first corrective attempts of Leo III. (right around 800 and Charlemagne). It gets very complicated, but its easy enough to tell the chances to get some kind of real clarity on the issue got `drowned out' by some bigger divides, and became a chasm that arguably should not be there. Some Orthodox even think understood properly, the filioque doesn't present a theological problem of the Trinity, so that just goes further to this point.