Mmmm. My only suggestion would be;
duplicate your layer twice
top layer: delete even lines (2, 4, etc) set new line spacing so that it matches up with the other layers
second layer; delete odd lines, set new line spacing – should be same as top layer – move lines down so they match up with layer 3
Turn off or delete 3rd layer (only needed to line up text)
Slide keyframes on 2nd layer so it starts 50% through first movement of layer 1.
There may be a simpler, more elegant way of doing it but…