Hi Brynn, ....
Would you know of any other settings that may still account for this that I have not tried.
No, this is really over my head, to understand how or why the quality of the filter rendering happens to create the kind of effect you want. If you really like exactly that effect, as I mentioned earlier, your screenshot tool was able to capture it.
Or else there are lots of sites where you can search for certain textures like that. The last time I was looking for something like that....let's see if I still have a link to one of those sites.... I think this was one I liked:
http://www.assistcg.com/With those comments, I'm trying to answer your original request to export a PNG, of a filter, with that kind of effect. Since a PNG is a raster format, and filters are really like raster contents, and Inkscape is a vector editor, Inkscape might not be the best tool to use. So that's why I suggested the texture site. But it's possible that I (or we) don't clearly understand what you're trying to do.
Lazur is really our filters guru, so those are some special filters which I wouldn't be surprised if he made especially in hoping to help meet your needs. I can't really do much with filters myself. (although I still hope to read up on it, and try it someday)
Another open source graphics program called GIMP is a raster editor, and I'm pretty sure it has a lot of filters as well. So you might look and see what it has to offer. I'm pretty sure you could use textures from the site above, with GIMP, and apply them to text. Although I couldn't tell you how, exactly.
Sorry, I wish I could help you better.