" This thread is about how to rearrange a tune while it's playing like suddenly deciding to skip a verse, extend a solo or you decide to cut it short and jump to the ending. I think Abelton can do that..."
Yep. It does all that BB Conductor does and much more. Not only does it allow verse, chorus, bridge, intro, outro, etc live control, it will sync video and lights to your show. It brings the miracle of the click track to life....
Click Track Workshop This video gives a complete walk thru and demonstration of a live stage show using live vocals mixed with pre-recorded vocals, live instruments mixed with live instruments and how to flow into and out of the click track, how to use the click track in conjunction with a cue track.
At around the 52:45 mark, the speaker gets into how to re-arrange a tune while playing live. Everything you question in your quote above is addressed in this video.
Regarding the cost of the software package, you are investing in yourself and a professional career. It is a tool that is necessary if you want to compete at the level as the band in this workshop. That means to me me the same as if you play electric guitar, you also have to invest in an amplifier. So, a satisfactory compromise to me would be to purchase a $600 Epiphone knockoff rather than a $1800 Gibson and purchase Ableton with the money I saved..
In your case, as a keyboardist, if you have 4 keyboards, you may choose to sell one to cover the cost.