If you are using the sequencer in Ableton all you have to do is turn off quantiziation then slightly drag the track until the peaks line up.

Other than that, all I can suggest is recut the loops. You could cutloops of a bar to fit perfectly, or if thats too tedious for or prone to error you can then cut a loop with a width of three bars then cut the four beats in the middle bar, and one beat to each side. That way you can use the sample editor in Ableton to drag the loop block forward or backward to emulate the same effect. By cutting a bar to each side you preserve any signal leading off the bar you are interested in (and in the intro) which will preserve a matchup of a loop.

You can do the same thing with individual samples as well by just inserting a bit of silence into the instrument then using the sample editor to define where it starts playing from.