Oh yeah see what happens at work.. I missed the obvious haha.. Just
select All, then move it, Logic will then definately ask you if you want
to move the Automation data with it..
Thats how logic always is - several ways. Actually I never use the Insert or Cut time commands. If you have a long note that stretches over a bar line, and you insert time does it length it or put an empty space there? And what about frozen tracks or locked tracks? I just end up doing things manually.