That sounds like a neat experiment. It's hard to know if it's safe without being there to smell it. But trust your senses, if it smells good and your gut doesn't give you a horrible sensation at the thought of eating it, maybe try a small lick and see how it tastes. Wait a while then try some more. If you do end up making cheese from it, let us know how it tastes.
The sauerkraut juice would be pretty acidic, so it makes sense that the milk would curdle. I've often wondered about using it to make a ricotta-like cheese, but then I find my vinegar and chicken out.
I think Gutted has a point about it being too low a temperature. There are some cultures that do well at room temperature (65 - 75 degrees F) but most of them like to be a lot warmer. When I culture milk at a lower than recommended temperature it ends up somewhere between a bit sour and quite bitter.
Maybe a room temperature yoghurt starter might be right for you. Though whether or not the word yoghurt is right for these milk cultures, most people call them that because they tend to have the taste and texture of yoghurt, and we don't have a better word for them in English yet. There is no special equipment needed, just a bowl, a spoon, and a space on your countertop. I like Fil Mjolk best because it's so flexible and forgiving. It' makes fantastic cream cheese.
A few things I've done with it so far:
http://wholewheatfsm.blogspot.ca/2013/11/some-amazing-things-you-can-make-with.html,
and a few places that carry it.
http://www.culturesforhealth.com/filmjolk-yogurt-starter.htmlhttps://www.etsy.com/ca/listing/20790710/fil-mjolk-yogurt-starter-culture-organic - this one shipps internationally.
Sorry I couldn't be more help, but do let us know how it turns out.
Doing my best to be the change I want to see in the world, one meal at a time.
http://wholewheatfsm.blogspot.ca
Currently Culturing
Kombucha, perry, cider, wine (red and white), mead(s), miso, sourdough, & seasonal veg my garden gives me