I've never used KILZ II, so I can't comment on the stuff.
However, if the objective here is to paint over glossy panelling only so that it can be stomached until it can be replaced, then I'm wondering if a better game plan wouldn't be to:
Prime it with Zinsser's Bullseye 123 latex primer, and then paint over that. Zinsser's boasts that their Bullseye 123 will stick to smooth surfaces like glazed ceramic wall tile, high gloss polyurethane, galvanized sheet metal and other smooth materials. I've never painted over a smoother surface with Bullseye 123, as I typically use it only as a primer over bare plaster or bare drywall.
However, it seems to me if we're using Liquid sandpaper to dull the gloss of the existing substrate, whether a more effective gameplan would be to use a primer that will stick well to that glossy substrate (like 123) and then topcoat over the 123.
I really don't know if this is a good idea or a bad idea. I'm just saying it makes some kinda horse sense to me.