Traditionally, academic disciplines have stemmed from others via discovery and innovation. There is no difference in academic CS; industrial (software) engineering best-practices, ex. design patterns, are derived from research. I would suggest doing a more thorough search through industry-focused academic literature, and pattern match what you do against findings to find a best match. Additionally, you could pursue a masters/PhD in a lab that does work on that topic (assuming you find something). Alternatively, get sponsorship from a company with resources as was suggested already. Think Bell Labs.
Out of curiosity, what is the general (or specific, if you feel comfortable sharing) area of your expertise? I'm always interested in exciting tech niches.
Unsophisticated users are exactly who I would be targeting. I would likely have to make widgets to integrate with common site building services like WP. An iframe is likely the simplest solution if they're building a site from scratch though.
The library alternative was suggested in another comment and is definitely a path I'll consider over a service. The goal of this project wouldn't necessarily be to start a business, but to help standardise how websites interact with sensitive user data.
Perhaps encrypting hashed passwords with a session key and matching against hashes encrypted with that key server-side would solve the issue you mention.
There is no reason to trust this service over Troy Hunt's API. In fact I would use his API if I could guarantee that I wouldn't hit the rate limit too easily, as I'd rather not come across as a spammer. I would reach out to him if I did end up using his API. A library seems to be a good (and more secure) alternative to a service, and is a path I will consider if I decide to start this project.
On your comment about sending hashed creds: credentials would have to be sent to some server hosting the database, as the database would be quite large (for example, there are ~500 million password hashes in Troy Hunt's V2 release). That is the only networked component of the proposed service. Everything else would indeed be done client-side (with the current feature set).
Bitcoin was not and never will be anonymous if a user converts to fiat. There is always a way to trace a transaction through the blockchain, and from there to a fiat-Bitcoin exchange where you have an account tied to your bank.
In response to answer 2: how do you account for the risk of storage invalidating stem cells after 60 years, if you've only experienced useful 30 year-old cell lines? Put another way, why would I pay $7,000 if neither you nor I knew if my cells would still be useful to treat disease when I'm 80, assuming I stored them at 20? Do you have a method of propagation in intervals, ex. thaw, expand each set of cells every 10 years, and re-freeze? You mentioned in an above comment[0] that you'd need a clinical trial to have the legal ability, so perhaps not?
Out of curiosity, what is the general (or specific, if you feel comfortable sharing) area of your expertise? I'm always interested in exciting tech niches.