Things have majorly improved for us too. Although dd has only STTN once (she was really sick so was extra sleepy), she often only wakes up ONCE or twice per night now, and if she wakes up more often (which does still happen) she is quick to go back to sleep with a short cuddle.
What solved things for us was night weaning. It was a complicated and NOT a linear process like ging said. We actually had to do it three times due to various regressions (sickness, teething, etc). When we finally did it and it stuck, it took an entire month of HORROR before we had an improvement. For that entire month, nights were so much worse than they were before and I wondered if I should regret doing it. However, we kept at it as we knew she could go without milk (she wasn't even asking for it) but is just a very stubborn girl. Once she figured out that there was no going back, she completely stopped waking up for those feeds. Unfortunately, she still seemed genuinely hungry early in the morning so we kept her 5 am feed which is what she typically wakes up for now. It has become too much for me as I am pregnant and my nipples are very sore. She will nurse constantly until 7 am when it's time to get up, and it's just too much for me. So today we explained to her that she is a big girl now and there will be no more milk in the mornings. The next little bit is going to be rough, but I do hope it will result in her sleeping even better in the long run!
And, as ging said, night weaning wouldn't have helped if she hadn't been ready (as evidenced by the fact that the first two times didn't stick as she just couldn't handle a night without milk when she wasn't feeling well). They do sleep better when they are ready.
Also: they do NOT need to fall asleep on their own at bedtime to sleep through. We still have to cuddle with dd until she is fully asleep, but she is able to put herself back to sleep in the night still.
They get there at their own pace! I'm so glad we just waited and didn't do any harsh sleep training.