There are much simplier ways of resolving this issue such as making it a legal requirement for those companies that provide employees liability insurance to keep an accessible unified data base (of those employers they have insured) on the web for 40 years. Of course that would be too simple and something the insurance companies will fight tooth and nail against, for they know full well that many employers will ignore the 40 year requirement and thereby make it difficult for an employee to make a far back claim.
I run a very small business with two employees. I am required by law to have employees liability insurance which is just as it should be. To prove this I am required by law to display (for my employees to see) a valid copy of the pertaining insurance certificate which again is acceptable.
However, by law I am required to keep each year's insurance certificate for 40 years. I am nearing retirement and my business will end with my retirement. As the law stands and for my particular circumstance, I will be required to keep the last issued certificate until I am 105 years old which is barmy. The chances of my living to this age are remote and what happens if I die before the 40 years is up I am not sure. Perhaps I shall have it stipulated in my will that the certificates be interned with me in my coffin so that those responsible will have to dig me up to get their putrifying paperwork.