Ableton Live nerd here.
For stop, you have different options:
I control transport in Live. GP is not synced with Link but MIDI clock through virtual MIDI Port. I don’t know the exact settings from mind, but GP starts/stops Transport/playhead fully in sync to Live without needing to wait the “Count-in” required in Link.
For transport stop in Live, I created a small M4L device that can perform it by automating a button. It could also be done with Follow Actions in Session View or another IAC Port that lets Live remote-control itself. There are plenty of YouTube vids available, however if you need help setting this up, don’t hesitate!
You could also do it the other way round, letting GP dictate the stop, but Live better knows when a song is over.
For your Rackspace change:
- Assign a PC number to the first variation of the desired song (not the song itself) in GP Setlist mode.
- Create a new virtual MIDI port for this purpose
- Create a new MIDI track in Live dedicated for the switch. Set input to “No input”, output to the created virtual MIDI port. You might need to enable the “Track” check in Lives MIDI settings for this port if it is not visible.
- Create a MIDI clip sending out the desired PC. Can be set in the “extended clip properties”, lower left part of clip view (Live 12).
- Put the clip in the arrangement position where you want to switch.
- In global MIDI settings in GP, activate the check for “accept incoming Program Change” for the created virtual port.
However, I don’t like it, as this can cause a lot of headache, e.g.: Live reaches end and sends PC to GP, GP selects next Song and sends locator CC to Live, Live jumps to next song and might skip everything behind the CC clip, e.g. the stop functionality, but dependend on the load time of the next rackspace. The stop functionality must be launched before the CC for locater arrives, but after PC is sent. You’re creating a race condition here.
Instead, I propose: Create the stop functionality and stop transport at the end of each song. Scarfice two buttons on your keyboard to step forward or backward in Song mode and declare GP the Master and Live the Sla…Follower 
And last but not least, why Session View: Because it is build for such stuff. You can rebuild every imagineable arrangement in Session View by using loops, independend clip starts and oneshot clips. Additionally you can set up on-demand Variation switching in GP (direct or quantized on a beat), quantized tempo switches, endless looping of a section, dynamic jumps to the next songpart, transport start, transport stop and a lot more, and all controlled by one single “thing that sends a CC to Live”. Or without any input fully automated, if wanted.