In Magi of Hermes, Aurulentus only spent 6 seasons stabilizing his research before success. How is that enough time to get sufficient points in his breakthrough? I feel like I'm missing a step in the rules for this.
In Aurelentus's write up it lists the six different effects he succesfully experimented on for his research. Meaning I believe he got six breakthroughs. Though he often needed to repeat each experiment until he got a breakthrough you only have to stabilize each breakthrough once. The Magnitudes of the effects ranged from 3 to Mag 8. That put's the total around 25 or more. That should easily cover a minor breakthrough.
I think it "feels" fast because everyone seems to want to minimize the warping points. But if you don't mind getting them (Because you are a P.C. and a young turk, etc.) Research can happen pretty quickly. It is a game after all.......
Look here for an analysis: https://forum.atlas-games.com/t/breakthrough-hermetic-teacher/8026/1 . The topic appears to come up regularly.