Doing this to a live show could easily make a phasey mess of everything unless you are only shifting d.I tracks or have near zero spill on the mics you are shifting.
A live show recording is supposed to be representative of the band playing live after all 
That aside my preferred way to do any fixing with free played audio is to first create a tempo map using time warp/warp grid. This way your grid follows the song tempo and you can use whichever quantise, warp or manual cut n slide techniques you like.