Another port that is typically not used much - external floppy port. I used to have AmigaLink which gave ethernet-alike network using the floppy port, and it was darn nice.
The floppy port can provide more power than the parallel port but I don't think it would be enough to run a Raspberry Pi, certainly not a V3. I suspect the max transfer speed of a parallel port would be faster than the floppy port. Also, DE-23 connectors are hard to come by

There's a similar project for the Apple ][ called Apple2Pi:
http://schmenk.is-a-geek.com/wordpress/?p=167. It uses a serial link to communicate between the Apple and a Pi at 115Kbps.
I think it would be much easier to build the higher level parts of this using a normal slow null model cable between the Amiga and Pi. The fast low level Parallel to GPIO protocol could be plugged in later.
I'd probably start by exchanging input events between the two machines so that a USB keyboard and mouse attached to the Pi can generate input events on the Amiga.
Cheers,
Andrew