just need to copy gates+envelopes+pitches from the guitar session, time-shift them

What is here "just" You will need three delays (one for the gate, one for envelopes, one for pitch) and  those three delays are not synchonized.

To say it in theoretical words: there is no difference whether you delay the command or the result. But in this case delaying the command is extremely complicated (think of the syncing), and will be very expensive: about 750 Euros for two voltage delays and one gate delay, versus 50 euros for a Behringer delay stompbox

Florian