Get the Mattuw's More Records v4 mod
audiomod
soundmod enabler mod

change any song of yours into a .ogg file and rename it to be cat or 13
same with the records in mattuw's mod except it will have to be 15, 16, 17, 18, 19, 20, 21
as well as with the Calm1, Calm2, and Calm3 so you should be able to have at least 12 of your own songs for beta

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Or turn the Minecraft Music off and play your own via Foobar or your favourite music player.