Welcome to The Bird Song Data 
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Currently trying to explore [http://birdweb.org BirdWeb] for their song library but wirelesspittnet is failing me per usual
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I Found an a song base from Arizona Field Ornithology. [http://www.azfo.org/SoundLibrary/sounds_Page13.html#Finches This] is the link to the finch tag, which is labeled "Fringillidae - Finches and Goldfinches" which I'm not sure is one of the species we are interested in. 
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I'm having some trouble finding info on galapagos finches specifically, I have [http://www.junglewalk.com/sound/Finch-sounds.htm#.WIGbiaIrKYU another] link to bird song but its again mostly house finches.
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Cool article about how the shape evolution of the beak also caused song to evolve: [https://www.sciencedaily.com/releases/2001/01/010111074902.htm Science Daily]