I don't know what your problem is with that cadenza, but I would start by not worrying about a fingering. You should rather be able to play this passage with any fingering, whether you just play 1 -5 all the way down in both hands, or change according to the sixths. This passage doesn't rely on fingerwork at all.
That said, anytime you play double notes, the trick to playing them well is this sleight of hand - imagine in two consecutive sixths, that the lower note goes to the upper, and the upper to the lower. I've attached a little pdf to show what I mean. If you approach double notes in this way, it is always much easier. It's a mental trick that relaxes the mechanism and allows you to lpay lots of double notes, quickly.
Enjoy.
Walter Ramsey