I don't know about the proprietary airbrush cleaners you've mentioned, but generic lacquer thinner will do the job more economically. Windex won't touch it at all.
Just a note about the bottled Tamiya Liquid Surface Primer. Though it's a lacquer based product, it can be removed (and at a pinch, thinned) using denatured alcohol (ie 90%+ ethanol). I use denatured alcohol to clean my brushes after using LSP and it works very well.
It also means that you can use it as a fillerand when dry, wipe off the excess with a paper towel moistened with denatured alcohol. Fill and clean without sanding. 
Note that this only works with denatured alcohol - Isopropyl, will not work for this.