However, the site will never keep the API's the same. The mini-program may stop functioning a few years after the person's death, and there will be nobody to change it
Organizations, trusts and even countries have been running for hundreds of years, based on a limited set of rules written in a programming language called LEGALESE, updated from time to time. One way to look at the mini-me program is as a "software trustee", whose parameters are monitored once in a while by a programmer-lawyer human. This approach yields the same scale-out/low cost/automation benefits of the cloud, letting a single programmer-lawyer maintain hundreds of trusts, in much the same way as a single admin can manage hundreds of instances in the cloud. It reduces the cost of creating and administering a trust to the point where such options are available beyond the top 1%.
Think of virtualization, emulators of old video game machines... they haven't been manufactured in ages, and yet, we find a way to faithfully run them inside emulators. I think we'll find a way to translate the Amazon APIs while remaining faithful to the original human's intent.