I've had some success at spinning juices in a centrifuge at 4,000 G's for about 40 minutes. You could spin at lower G's for a longer time, though. This will remove insoluble particulate, which especially helps with natural juices that have been strained with mesh - not nearly as effective as a centrifuge. It's ineffective, though, when you're dealing with dissolved substances like polysaccharides.
As a chef, I have a centrifuge large enough to use for production cooking, but smaller centrifuges are available on Amazon for around $100 that will spin very small amounts of liquid at high enough speeds.
As far as the ultrasonic cavitation, the low-powered models probably won't get you the breakdown you need, and that's assuming that the smaller particulates still won't clog a wick. I'm not sure how many microns are allowed
through a fiberglass wick, but I'm positive 400 mesh will allow a much larger particle size - which I can confirm anecdotally. You still, then, get caking on the coil - not really winning.