Blockchain, indeed, would be perfect for this. ...
That would require a system of maintaining, publicly available, the data and methods for experimental procedures. These are massive heaps of data. That doesn't have much to do with blockchain, right? How would it be handled?
Well I like to think that blockchain IS in fact a great fit for this. Take a look at projects like Hinounou (saw it mentioned above) that are already addressing chronic/rare diseases. An intelligent data platform that securely facilitates the storing and sharing of the Seniors’ health data via blockchain, with individual records stored on side chains to preserve the consumer’s rights to privacy, erasure of data and the right to be forgotten. I think all the requirements that you mentioned are solved and addressed by blockchain, by I could be 100% wrong! Let me know what you think!