One item tried in industry was to take good quality water and run them through filters small enough to stop microbes ( the last I heard, about 0.2 microns, but it Could have gone smaller). This was sold as a time saver over the normal approach. But it didn't work. Might be a viable approach , if you weren't in a hurry.

@Ag8n Thanks for the suggestion to use nanofiltration! I think the main impurities are the electrolytes (e.g. K+ and Na+ ions) that are added into bottled water for taste. Do you know what water purification method works best for removing them? I am thinking along the lines of some kind of low-cost ion exchange system, but am not sure what specifically.

Yes, ion exchange is a good idea. Usually, it's cation exchange, anion exchange, and actived charcoal, followed by the particle filter. A conductivity meter usually follows as a sanity check. You have to do testing per appropriate sections of the USP/ISO for sterile water and/ or purified water. Plus testing for the solution. Anything you can do to extend the life of the ion exchange will save money!