I think you are just fallowing the original ground and the one that was added by the previous owner. There is no way for the head unit to supply power to the amplifier. TO be sure, pull the fuse out of the little fuse holder by the battery. This is for the yellow wire hooked directly to your battery terminal that is incased in loom.
Once pulled, the amp should not power up.
The power wire as installed by mazda runs through the firewall, under the carpet, along the side sill, under the rear seat, into a strange plug in clip if memory serves, then from there it goes behind the plastic and carpetin the trunk, up behind the enclosure and to the amplifer. It should be yellow the entire way.
If you can, get me lots of pictures of all the wires your finding and I'll try to sort it out for you.