As Guido stated, check the plugs, Some of the ANALOG settings cause this but turning them off will lose some character which you clearly wanted.
On your master track use Volume Automation in Logic at the intro and outro if you prefer. I have done this many times as the hiss is only evident when all the music is not playing. Your Automation moves need to be MACRO tight ZOOM in as far as you can and ride up just before your first Transient at the head of the track. Play around and see if you can accomplish what I am taking a very long time to explain. LOL
Hit me up if you can't, we can connect and work it out!