Finding ultra-pure water locally...

Dumb question: how exactly do you "rinse" the record?

Drubin: Carefully douse , paint, or spray a portion of the LP absorbing the water with a micro cloth. Or, repeatly spraying pure water on a revolving a disc seated on a RCM, then vaccuming the disc to remove the water and any contaminates. Some record steam cleaners report dipping the LP into a shallow bowel of pure water , rotating the disc with a micro cloth in one hand to absorb the water from running over the label. What ever you decide , experiment with a trashed LP to perfect your hand-work.

Drubin, my process for rinsing with a vacuum cleaning machine is to dedicate a cleaning pad (Walker Audio, Disc Doctor or Music Direct) to the final rinse; apply ultra pure water to saturate the pad; apply pad to rotating LP; then vacuum.
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With the record mounted on my Loricraft, I squirt water on it, then turn on the platter and hold a carbon fiber brush to the surface so the water gets distributed as the platter turns. Then vacuum off the water.

Drubin,
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The Axiom everything matters especially applies to cleaning records and the sonic results that are yielded.
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I use a separate brush for each fluid and or rinse that I do. I don't want to cross contaminate from one step to another. Using "Ultra-Pure" water matters dramatically in each step (either as part of the cleaning solution or as a rinse).
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Using a strong vacuuming machine (Loricraft or other) is important in that you need to remove all of the cleaning/ rinse solutions off of the record to take the impurities /dirt/ mold out of the grooves.
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My great preference is the AI solution system as I have mentioned before. Walker's system is quite good as well. The more resolving your system the more you will appreciate the value of good cleaning / rinsing solutions and a great machine.
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Good Luck
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Rgds,
Larry