Have you tried the traditional ways that the French and Germans eat it? If you braise it, you're going to lose the "live" aspect, but you could try very lightly cooking it, or kind of running with the traditional theme and just serving it alongside some of the traditional meats cooked with it - rich, fatty meat. Bratwurst, knockwurst, kielbasa, pork belly, pastrami, pork shoulder, etc - the kraut is a nice foil, and the sour is a little more welcome.
Have you tried eating it with some sauteed apples? That's pretty common and would sweeten it up.
Oddly enough, the way I've enjoyed it most is sort of as hangover/too much wine food with some non-red-meat-eating friends. After lots of wine all night, we had a late night snack of sauerkraut alongside some turkey pastrami. It was surprisingly good.
I'm making my first batch of "real" sauerkraut now, and I'm really curious to see the other answers. I also struggle with a lot of fermented veggies. They are just so...pungent!