If you don't mind the pattern to remain at the same location, relatively to the background, this is a possible technique:
I exported the individual frames without fills to PNG files, filled with a pattern in an image editor and re-imported the image-sequence into Anime Studio, using the import image sequence script. It is a strange effect, and for that alone, it might be useful.
(BTW If you select the empty fill, enlarge the selection by 2 pixels, so you don't get any closure errors at the edges.)
I created this pattern file to fill:
BTW2 I tried both region binding and flexible binding, and both have the fill bleeding into the edges if you warp your texture fill too far. The effect is less in flexible binding, because it doesn't warp the vectors as far as region binding. If you bend a little bit further, so you get the same distortion as region binding, things get just as bad with flexible binding.
BTW3 Perhaps the best method is to export to PNG files, do some image editing, to remove the irregularities, and re-import as an image sequence.