Honest question, is there a way to run the entire process acid-free?
No. Silicon oxide (glass) is extremely tough from a chemical perspective. That's why it's used in chemistry for everything. Barely anything touches it. Also this is the main reason I think that the meme of "silicon based life" is completely absurd and comes from people who only took high school chemistry and built their worldview on that.
No acids at all? That would be stupendously difficult for no real benefit. So many things are acids, so many useful reactions involve acids, and there's not a significant correlation between "is an acid" and "danger".