The reason, as a general screen-printing practice, that the stencil is on the print side and not the inkwell side is so that the act of the repeated pulling of the squeegee doesn't damage the stencil. Imagine how quickly details would be scraped-off as it pulled across. By having the inkwell be just a smooth surface of screen the pulls will be smooth and unimpeded. Even in the photoemulsion process where the stencil is more or less "in" the screen, it is considered best practice to build a thicker layer of emulsion on the print side when coating. Hence a common coating pattern of "bottom-inkwell-bottom".
Re: the sticking of the powder/frit color that's not really an issue. Especially if, after reclaiming the excess powder, you tap out the screen then rinse & dry it thoroughly before a color change. At that point, anything that's stuck in the vinyl adhesive is stuck for good.
Again, if you're doing longer production runs consider creating the art in a photoemulsion stencil. It's significantly more durable and more easily repeatable compared to hand-cut vinyl. If you like the hand-cut look you could create the art in Rubylith and use that as the positive to burn your emulsion-coated screen.