Hi beaur, that's great that you've got access to lab-grade water, as really pure water is a great natural solvent to dissolve dirt and contaminants!
I used to buy NERL lab water in 5-gallon "cubitainers" but given the cost (and shipping) I now have RO/DI filtering equipment at home, to make 0ppm RODI water from distilled supermarket water..
I'd recommend you buy a TDS meter, they start at only $15 and a decent one like the HM COM-100 is about $60, which is what I use, it resolves to 0.1ppm. You can easily take water samples from your Klaudio after cleaning a few records. I think you'll be surprised how quickly the ppm's go up..
I change my water often, sometimes after just 10 records, even though I'm usually cleaning first in an Audio Desk machine, so the records are already "clean".
I refill with 0ppm RODI water that is preheated, I use a small aquarium heater in a 2.5 gallon bucket, holding a gallon container of RODI, so I always have water at working temperature, ready to go..
It's all in the details, and I think using (consistently) pure water is one of the important ones..