You have a variety of options open to you here I reckon...
You could whack the ship miles into the distance over a couple of frames and use the lazy points plugin on it to get the stretch.
you could deform the ship and use it as a morph target - have it first morph to your mega stretched ship and then morph your stretched ship back to the normal one in the distance.
You could try using a deformer directly within Layout
for the warp effects whilst the ship is in warp best way I think would be to build a tunnel of single point poly's - make them luminous
(stars essentially) and then move the tunnel of stars and keep the ship
stationary.
Two or three tunnels moving at diff speeds would add to the effect each slower moving tunnel sequentially larger than the prior one.
There are no doubt many other methods I can't think of at the moment!