The longer the final snake is, the easier it is. It does need to be at least 4 squares long.
What you should do is get the snake onto the column east of the entrance square, and make sure it is chasing you north.
When you get to the snakes first v-pref move:
Step west. The snake should move north next to you.
Step west. You are on the same row as the snake, so it should move west towards you.
Step south. The snake should move south next to you.
Step north. The snake wants to go north but can't. It tries N, E but those squares are blocked by its own body (which is why you need 4 length). So it keeps heading S
Step NE. Now you are behind the snake so it will keep heading south.
Wait where you are and it will keep heading south and into the dead end.
This is roughly what you want to see.
I started a snake-training hold at some point. I should finish it.