Blocks display on "All pages except those listed" unless it is a Search 404 page

The Search 404 Module essentially creates urls, from misdirected/missing urls.

Because of this I am noticing a problem with my blocks that appear on Search 404 generated pages. I use the "All pages except those listed" option when displaying certain blocks, e.g. search block. However, because I cannot account for missing/fabricated urls that are generated blocks I do not want to appear on the page show up anyway.

The possible solution I see is to either switch all of my blocks to a "Only the listed pages" option, or create some sort of Search 404 directory in the url

Example:
User Inputs : example.com/unknown-page
Search 404 returns: example.com/search404/unknown-page

This would allow me to account for and exclude Search 404 generated pages by adding "search404/*" to my exclusions list.

If there is some other way of doing this, please let me know.