First of all, I can only do one slimeling runs every two days anyways since I need to bank up turns (no way I can get the turngen needed for the tube and the 42 turns on llama gongs while being forced to use up the majority of my fullness/drunknenss/spleen on slime consumables).
Anyways, when you see a pristine slime tube (no one had spent any turns on it), just max out NC and keep +ML 0 or negative (if you have a space trip safety headphone, it's perfect for this task), free runaway in the tube from any slimes you encounter (if you don't understand what free runaways are and don't want to look it up on the wiki, then stock up on tattered scraps of paper and spam them when you encounter slime monsters), until you encounter the non-combat Engulfed!. Choose to squeeze the bladder, and after that you're done with the tube - I'll clear it and give you the larva when I'm done. Coated in Slime will hurt you at the beginning of combat for increasing damage as its duration gets lower, so either time it out by doing non-combat related stuff, or take a bundle of chamois from the clan stash, use it, and then click on the bucket to choose to wipe the condition. The Hot Tub in VIP lounge will also remove it if you have access to it.