Hey @Alex_Knerzer, welcome to the forum!
This might be something you can already do in Live. I see two potential solutions to your challenge.
First, you could create multiple audio tracks for the different song intros and unmute the one you’d like to use. This is fairly simple to set up but requires a bit of work every time you change the order of your songs.
Alternatively, I like use a drum rack that contains the last few bars of the song which I can trigger before the SONG END marker. These samples run independently of the playhead so they don’t get cut off when AbleSet jumps to the next song. Here’s a video showing what I mean:
I hope this helps!