i think all you need to do is transition from the first comp to the second at some point between 3 and 7 seconds into the timeline, and then add a simple expression to the second comp to make it loop.
to make the second comp loop, enable time remapping (layer>time>time remapping) and then add an expression to the time remapping property (select property, then choose animation>add expression) and type or copy/paste this expression into the field:
since you are looping a comp (rather than footage) there is one other step. go to the last time remapping keyframe. move one frame before that key, and add another key (right-click on the time remapping property and choose add key, don't move or copy/paste a key). then delete the last key frame.
now, if you lengthen out your comp, you can drag the endpoint of the second comp for as long as you need, and it should loop continuously.