Special purpose IP address registries are maintained by IANA.

IANA is a function operated by ICANN on behalf of the IETF and the relationship is governed by a legal agreement between ICANN and the IETF, signed on March 1, 2000 called "IETF-ICANN Memorandum of Understanding Concerning the Technical Work of the Internet Assigned Numbers Authority":

https://www.icann.org/resources/unthemed-pages/ietf-icann-mou-2000-03-01-en

Registration of resource records is covered by section 4.1:

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The IANA will assign and register Internet protocol parameters only as directed by the criteria and procedures specified in RFCs, including Proposed, Draft and full Internet Standards and Best Current Practice documents, and any other RFC that calls for IANA assignment. If they are not so specified, or in case of ambiguity, IANA will continue to assign and register Internet protocol parameters that have traditionally been registered by IANA, following past and current practice for such assignments, unless otherwise directed by the IESG.

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The document "ICANN Controlled Interruption IPv6 Research Study - Report 2" states the following item as a deliverable:

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4. A clear recommendation to ICANN regarding what IPv6 address to choose for controlled interruption

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Given that there's a legal agreement in place regarding the operation of IANA by ICANN, it would be advisable for the Research Study authors to talk to ICANN legal to see if this recommendation is compatible with the legal agreements in place between ICANN and the IETF.

In other words, if ICANN wants a specific addresses to be reserved, that needs to be done via publication of an IETF RFC, exclusively using IETF processes.

At a practical level, the starting point for the suggestion to use ::ffff:127.0.53.53 or ::ffff:7f00:3535 would be to write an Internet Draft to be published as an appropriate RFC to reserve the IPv4 address 127.0.53.53. Once IPv4 registration is complete, the ipv6 registration should be straightforward