Ms Katz, I believe this shall be, as they say, the start of a beautiful friendship.
Correct. I have had little motivation to search for a way to brew these potions without magic, though it is on my rather long list of things to experiment with. However, converting the potions using magical ingredients to being able to use mundane ingredients and a small private medical puzzle have currently been occupying the top spots thus far and look to do so for some time.
I shall put together a crash course, so to speak, in regards to the ingredients, magic and how they interact to create the potions. Once you have had the chance to start reading that, we can begin translating magic into science and science into magic. There have been attempts to do that in the past but they have largely ended in frustration on both sides.
There is a tendency on the magical side, when something works and works consistently and without deleterious side effects, to simply accept that it does work without questioning why it works. Combine that with the fact that many potion masters and mistresses and spellcrafters are highly secretive about their work and that there is no real equivalent to the Muggle system of "peer-review" despite many attempts to establish such a thing and you can see how things can become problematic.