I think there are quite a few companies like this in various countries, away from SF PR that we don't know about.
https://www.broadinstitute.org/about-us
https://broadinstitute.wd1.myworkdayjobs.com/broad_institute
I work there. My group builds scalable tools for genomic data analysis:
We're about to post two job reqs, for an SRE and front-end/design position. Email in my profile. Get in touch if you're interested.
gnomAD is the largest public dataset of human genetic variation:
https://gnomad.broadinstitute.org/
They recently a 7 paper collection in Nature: https://www.nature.com/collections/afbgiddede. They're also hiring an SRE:
https://broadinstitute.wd1.myworkdayjobs.com/en-US/broad_ins...
Lots of other jobs at various levels throughout the institute. Biology knowledge generally note required (I had none), although it helps (but be prepared to learn).
The primary way that I find companies is by watching conference/meetup talks from highly technical conferences that overlap with my interests. If the talk is on something that I find particularly interesting then I add the speakers company to my list. And then use tools like LinkedIn to find similar companies and assess them if I want to grow my list.
For the type of hard works that you're describing, the most common funding model I've seen is through sbir and sttr government grants. There are a lot of small companies that are funded this way, by necessity of those grants only being available to small companies. Eastern Foundry is an incubator for these sorts of companies
They're also groups like Microsoft Research and Pixar, that are internally funded, and some startups like Amira Learning, drone seed, and saildrone that look more funded by backers. Finally Lincoln Labs, UW APL, and JPL act as industry-focused research labs associated with a university.
Galois is an Oregon Graduate Institute spin out, and Grammatech is a Cornell University spin-out
You won't find many. By definition what you're describing is incredibly expensive and without an immediate return. So the only groups that can afford work on these kinds of problems are academics, big companies with large R&D budgets or organizations like NASA or CERN. Any small company that attempts this will just go broke very quickly.