Maybe I'm totally wrong here. If so, you really should make your crawl corpus publicly available. Trickle it into one of the public clouds and charge people a few microcents per query. You'll get to retire early, knowing you've done a good deed for human technological progress.
> There are websites that give you different results depending on what time of day it is, or where you are from.
That has been true since at least 1993 [2], before there were search engines!
> The hard problem of search engines is to find a good subset of the internet for some definition of good
This really is a case of the tech industry trying to redefine "search" in a way that gives them editorial power. Librarians don't do that sort of thing. We could learn a lot from their integrity. Or we could just stop calling it "search", because that's not what it is anymore. For example, that box at the top of amazon.com is most definitely not a search box anymore; it's a sales-lead-generator box. The button should be marked "try to sell me shit which is not necessarily related to these words" instead of "search".
[1] off the top of my head: archive.is/archive.today, gigablast. I'm actually having trouble remembering any still-operating whole-web crawlers besides Google, Bing, and Yandex.