This way is slightly faster and easier to do imo:

Get to the green voice computer and when it says hello, say Hello and slightly after Do it, then say All of ya before it teleports you, so the slig won't run away. Then say Help, All of ya, wait for both sligs to do that greeting noise and then quickly say Do it Do it and Kill 'em, wait for slig to start laughing, say Follow me, do a hop and step to left and wait for him to come.

Say Do it, as you get to the lower screen, say Help and Do It again, the same above. Then as you get down again do a hop, wait for slig to come to the lever and then do another hop back to the elevator. If the coming slig is too slow and you're too fast, he might slide to the left, if it happens, wait for him to come next to you, then say Wait and you can do the rest the same way. Say Do it, then All of ya, wait for elevator to come up slightly, then hop and say Do it, then All of ya again quickly and Do it again, so that the left slig pull the lever twice, then wait for the lower slig to come to the lever say Do it twice, to make both pull the lever only twice, to make the dogs disappear.

Then say Kill 'em to kill the dogs, All of ya and wait for them to greet you back, then Follow me, step to the left and three hops to the elevator. Say Do it Quickly before the second slig comes, so he won't disappear. Then wait for the elevator to come down, say All of ya, make a step to right and Follow me, then All of ya again, wait for them to greet you and quickly say Do It, Do It and Kill'em. Wait for the slig to stop shooting (the animation might take longer sometimes) and you're free to go. :)

Now Sometimes the second slig is slow coming to the last elevator and he will land on the left side of it, in that case, do a step to right, turn around to face him and say Follow me, wait for him to come to you and say Follow me again so he will come back to the middle, while the elevator is still moving and both sligs will line up properly. Then as the elevator stops, make them follow you and then it's the same. If somehow you managed to get one slig facing the other way next to the last lever, either line them up properly again or say Do It twice with a bit of delay between the inputs and it should work, but it's a bit harder.

If you have troubles with the last slig disappearing, you can wait for both sligs to come to the middle properly, then say All of ya, wait to greet you and then Do It and both should be pulling the elevator and stay. Or you can make one slig be in the middle and the other either on the left or right. If it still disappears somehow, just go back up, say Help again and make him follow you again. Or you can still get it done with just one slig, but I dont really recommend it 'cause it needs to be timed really well. Or then just killing the slogs normally with one slig.