How to select ways that are NOT in specific areas?

There are some unclear issues related to your question like: what is the "outside" to your original area (the complementary area relative to the whole Planet or to a larger rectangular polygon enclosing you area), what with the ways crossing the area... just to mention some. Anyway, assuming that the query/filtering model you have mentioned works properly here are some hints/options:
-Using a larger rectangular polygon and your query model select the ways inside the rectangle. So, subtract from that set of ways the ways you have already as a result from before.
-Create a complementary area to your original area and run your query using this as the area argument. To create the complement area is rather simple. Take the larger rectangular polygon and tag it as outer. Add to this the polygons from your original area with opposite rules. This multipolygon now probably represents the "outside" of your original area.
However, be careful. If the set of ways to filter is large and so is the outer polygon of your original area, the procedure to accomplish may take many, many hours. In similar cases you need much more robust and specialized filtering/extracting models than the one you have described.