The rapid advancement of generative artificial intelligence (AI) has intensified debates around who controls and benefits from the data used to build AI systems and how it is obtained. In response, visions for building public interest AI ecosystems are emerging, which aim to promote data and AI as public goods and enable diverse voices to shape AI development. This paper presents findings from the Choral Data 'Trust' Experiment, a pioneering initiative by Serpentine, a UK public art institution, to test new approaches to governing AI training data through a real-world case study with 15 UK choirs.