If you're willing to release the database or at least the scraper as FOSS, I'd be willing to try making it distributed. The way this would work is:
Users opt-in to storing part of the index on their machine
Official servers are just relays to a network of these users
Frontend JS would be necessary to stream the results from the network
I also don't know the profit model here, but costs would be quite low since you'd only need geographically distributed relays with no storage requirements and minimal processing, though bandwidth would be quite high (I think bandwidth could be reduced with something like WebTorrent). I'm thinking maybe users could pay some nominal fee ($1-2/month), or get the service free by agreeing to host data (to seed, you would provide a few nodes with the full index; these could be removed once enough people sign up).
I'm working on a related project right now (distributed Reddit alternative), but a search engine project may be faster to get off the ground. Updates to the index would use the same network.