You can always create keyframes while the text is parented and then unparent. Or you bake the keys using the respective keyframe assistant based on a dummy expression for the position. Beyond that I see nothing complicated in your video and it could just as easily be hand-keyframed.
Animate the blue layer. Parent the text to the blue layer. Find the point in the animation when the text is at the precise center. Split the text layer. Un-parent the new text layer that results from the blue layer. Done.
When I do things like this I use an expression and a layer marker. You put the layer marker on the layer that is moving and add the expression to the position property of the layer that is following. In plain English the expression says take my position from the lead layer until you reach the time value of the marker then keep my position at that value. This is done with a simple if statement that says "if time is less than the time of the marker my position equals the leader's position but if time is greater than the leaders position make my position equal to the leader's position at the marker."
You simply use the anchor point to adjust the relative position of the follower and move the marker to the spot in the timeline where you want to drop off the hitchhiker.
To avoid the syntax errors I am not going to post this expression now because I am replying with my phone using voice to text.
EDIT: In front of a machine now so here's the expression:
lp = thisComp.layer("Leader").transform.position;
if (time <= mrkr)
P = lp
And here's a project.
(note: Dropbox will probably add a .txt extension to the file name. Just delete it and you can open the project)