if another interrupt was called, it would interrupt the interrupt, stopping playback, which defeats the purpose entirely.
Why would it stop playback?
That quadrature decoder looks promising and I've seen it before, but I'm having difficulty figuring out from the datasheet alone how to hook it up and what exactly the output is. Is there a resource with examples on these?
They're very simple devices. There's billions and billions of examples on the web.
Misunderstanding of how interrupts work goes hand-in-hand with misunderstanding of why and whether it might be desirable or in fact undesirable to use interrupts at all.
Interrupts and mechanical switches are rarely a good combination. Switches bounce and cause dozens of interrupts when they're switching, causing as many problems as they solve.
(...and "Hardware debouncing" belongs in the same category as using interrupts with switches - sounds good on paper, terrible idea in practice)