I believe that the parallel port was not intended to do much more than transfer 8-bits to a printer; while it has been used for Zip drives, AV A-to-D digitizers and the MAS device, that was not its designed purpose. DMA to a high speed parallel "pipe" occurs for SCSI, but PIO is used on IDE. The other DMA devices are serial in nature. In any event, you are using the Amiga as a storage device to feed data to an MP3 chip and there are choices made based on cost and simplicity. PIO is also used in place of DMA for serial USB and Ethernet devices (see Jens' articulation on EAB).
The function you desire would be best handled with a sound card with the desired decoding chips in situ.