Does anybody have any recommendations for a Swagger-style documentation toolchain for REST APIs? I mean actual REST, not this weird anti-REST where you predefine fixed URI structures up front.

REST APIs are based around media types, not URI structures. Unfortunately, tools like Swagger are based around URI structures, which shouldn't be in REST API documentation at all. It makes trying to find good tooling for REST APIs difficult when people say "just use Swagger" and similar.