Half-Blood Prince clearly shows that Snape's instructions regarding 6th year potions are superior to those given in the books, so much so that just blindly following them without even understanding the reason behind them lets Harry make better potions than Hermione. It's also heavily hinted that Snape invented or discovered these techniques himself, most likely while he was using the books as a student himself. Some of these techniques are so unorthodox that Hermione doesn't want to follow them, nor does she want to believe that they work.
Did Snape ever teach any of his discovered techniques to any student? Perhaps to students of Slytherin house, or in special classes to Malfoy?
There doesn't seem to be anything indicating Snape taught the techniques from his copy of Advanced Potion Making. However I would disagree that we have proof Snape invented/discovered these techniques.
Potions is generally billed as being the equivalent of a chemistry class, where students follow specific directions to observe specific results. However by NEWT level that does not appear to be what's happening.
For example in Harry Potter and the Half-Blood Prince Slughorn states that "by an almost alchemical process" a student can divine the extra ingredient needed to create an antidote for a multi-poison potion. He also claims in his first class that he "does not expect" students to create a perfect potion even though they have step-by-step instructions and all the ingredients to do so. Later (forgive me I don't recall the exact quote) Slughorn expresses the thought that a "real" potion maker needs independent thought.
Therefore I submit that, at the NEWT level, the potion instructions are INTENTIONALLY DESIGNED to create not-quite-perfect examples. Students are expected to either use the theory to determine what extra needs to be done, or presumably the not-perfect potions are discussed in lecture.
Hermione not being able to progress beyond the given instructions even though she memorized the theory (and remember even in their antidote-making class she doesn't seem to get it quite right) is in keeping with her coming in second in Defense Against the Dark Arts, where her problem of turning "book smarts" into actionable results also comes into play.
Therefore I submit that Snape's notes in his textbook are more in keeping with a cheat-sheet of answers rather than "new techniques" and teaching them on the "front end" would miss the point of the practical potion-making exercises.