Greasing my hair down never worked. It was always a very fine-toothed comb and an hour.
I have soft, baby fine hair that was easily and frequently tangled when I was that age. (For the same reason, if I remember correctly! And those were the days before damage-free rubberbands.) We used all of those items you mentioned, but what worked was a lot of patience. My mother would just very sternly tell me that I had no choice but to sit still and made it a lesson. I would sit between her legs on the floor while she worked. I hated it and I fidgeted, but I learned from those experiences that my hair was more fragile than most. My mother had the woman who cut my hair teach me how to brush it properly so that I could best avoid knots and breaking my hair when running brushes through it. I think that because getting knots out was misery, the lesson stuck.
Here's what I do: When trying to get the knots out, take the mass of hair and the comb and first pull down very gently with the comb as far as you are able to with the hair still slackened. Be careful not to yank and tighten the knot. Then hold the mass of hair at the ends between two fingers of one hand and above your fingers gently comb upward on the hair (almost like you would if you were teasing it, but don't too push hard. I hope that makes sense.) You'll have a small amount of hair still between your fingers at that point as some of it will have pulled free. See if that loosens any of the knots. If it does, gently pull the freed hairs away from the mat, using the tip of the comb to grab them and repeating the process until you are left with a few very small impossible knots that you can't get out. These you can cut without obvious damage or perhaps you'll get lucky and can do it until they are gone altogether.
Every once in a while I still get a bad knot and handle it like this. I've already had to put it into practice with my 3 year-old who unfortunately has my hair and likes to play salon, too. It's going to take some time if it's that bad, but it's worth it to save as much of her hair as possible. I wish there was an easier way. I'll be really interested to read what everyone else posts in the hopes that I can find a better method, too! Good luck!