Considering the butcher's nails are essentially a drug, World Eaters are pretty much drunk all the time... oh that xD
This is easy to solve. World Eater kills and eats the puppy, kills the psyker and burns most of his body away. He will then proceed to pick up the ultra light charred remains devoid of fluids and use his assault pack to jump over the river. All 3 are on the other side, the condition of crossing alive was never mentioned.
I need no transport. I come from the warp! But yes, I would trust the marines of the brass to carry me around.