Frap, I used to use the rinsing with distilled water method, and TOTALLY agree with your comments as to the sound quality improvement it provided. I now have a new method that does not benefit from this and will explain.
I use Record Research deep cleaner with my VPI 17F, and a pickup tube and mount with the number one marked on top. After three rotations in each direction with the fluid, I vacuum for six rotations. Then I use Record Research Image Restorer, three rotations as above and 6 rotations to dry. Then I apply Last Record Preservative with a small short nap applicator and after about 20 seconds, I replace the pickup tube and mount with one marked number two. I then re wash with Image Restorer and dry six rotations again.
If the LP was really dirty, I use First, (brand name) with it's applicator and brush into the grooves until all the dirt and mold release compound is dislodged. When First was banned by the EPA ( Freon based) , I bought about twelve bottles, but I am now running low.
On all the above procedures, I use the built in VPI brush for the number one session, and hand hold a brand new VPI brush for number two session. When complete, the LP goes into a new paper sleeve and I replace the record jacket's outer plastic cover. I have a labeling program in my computer and generate stickers that indicate the level of cleaning procedure ( simple check boxes ). I also label whether the LP is an original, an older reissue, or a modern reissue. I even have labels indicating Promo and/or DJ copy, and 45 RPM. Obviously these stickers are applied only to the protective plastic cover, and not on the album art.
A valuable aid in the restoration of old and sometimes very dirty LP covers: Buy the Plexiglas cleaner, Novus Plastic clean and shine Number 1 ( not #2 or #3!) and spray a light mist directly on the cover. Immediately wipe with a clean cotton cloth, until the surface is clean and polished. It is easy to restore a pretty nasty cover to almost new condition. The varnish and dryers in the inks used to print these covers are usually aged and become faded, in addition to drying out. The polish will not restore color where it is totally absent, but it will improve what is there by an amazing degree, and without any harm whatsoever. Old albums that appear to have a plastic like finish on top benefit the most from this, with the dull paper like classical labels with their absorptive open pore finish, improved the least. Hope this helps you as much as it has me!