Mixing up AP adventures, or even adding in other extraneous adventures to pad out an AP, i something frequently done, at least according to many forumites. I suggest using the specific forums for each AP you want to mix.
Simultaneous campaigns. Most APs have natural breaks between books or between chapters. If your players have hit a wall with one, then shunt them to another so everyone gets to keep having fun. Legacy of Fire had those time gaps, particularly between AP13 and AP14, and Skulls & Shackles felt like bolt-on encounter sandbox. With the Genie shenanigans prevalent in LoF, whose to say they don't have access to Teleport across Golarion? Major City to Major City restriction would limit Player shenanigans since a dominant feature of Skulls & Shackles is the exploration and subsequent ruin-clearing.
LoF I remember as being a Bonanza of items, while S&S felt very disjointed to me and padded out in encounters to level the party up for its finale. With Legacy of Fire phases thrown in, you can SKIP the nigh endless "random" encounters PCs will spend in the ruins within S&S and focus on the fun trailblazing.
I haven't done this exact course of action myself (splicing two APs), but something similar. When the group split up among party lines, rather than re-roll my faction chose to take our characters to another AP. What was set in Ustalav (Gothic Horror inspired by Carrion Crown AP, Rule of Fear CS, Guide to the River Kingdoms CS & CASTLEVANIA lol) now became set in Cheliax as we began Council of Thieves.
