In my opinion a MC should have at last one alchemy or material based virtue initiated before teaching Lesse Elixir what is now given. That why I think the new one look better as it also would allow you to initiate other magus not just new apprentice into the MC.
I don't see how the Alchemy path synergize with the Arithmetic Path but that is no problem for me. Vulgar Alchemy would help your Lesser Elixir but I also don't see it as must for a alchemy based MC to teach it.
What you probably need to think about is the relationship of The Cult of Alchemical Numerology with The Order of the Green Cockerel (teaching nearly the same things especial the income source Lesser Elixir and the Greater Elixir as the end on the path) and the Arabic Alchemists (Are be said to be superior to the western alchemist).
Edit: You maybe also want to read the most recent discussion about Hermetic Architecture https://forum.atlas-games.com/t/what-is-hermetic-architecture-for/11611/1 from this it sound that we need to at last house rule that you also can do Boundary size with it.