Honest question, is there a way to run the entire process acid-free?

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".

yes acids capable of etching = danger :) aktschually

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.

Is it conceivable that some organic solvent could be synthesized that is, simultaneously harmless to water-based biological life, and capable of etching Silicon oxides?

Not really. Organics don't really have any affinity for this type of compound. You could, of course, create some kind of organic fluorinating compound, but it would basically just put you back at square one for safety.