Procedure:

The above 2 parts can also be bought from a Best Buy store, or can be ordered from many car audio shops.

Wiring the harness is simple. Each harness has wires with similar SOLID colors for power and ground, and another set of color and striped wires for the speakers.

Connect each color of wire on the 1784 harness to the color that matches on the 1770 harness, with ONE important exception: The YELLOW and RED wires must be swapped (yellow on the 1784 to red on the 1770 and vise versa) - THIS IS VERY IMPORTANT, because if you don't wire it like this, the blau will pull it's main high-draw current from the "switched" wire which is just meant to be a signal to turn the radio on and should not be relied upon for operating current.

There's 3 orange dimmer wires coming off the 1770 harness, and only one coming off the 1784. I believe the one on the 1784 is Orange with a white stripe. Match this up with the Orange/White wire on the 1770 harness, and either remove the other 2 orange wires from the plug (requires you to take apart the plug), or cut them short and cap them with a crimp cap or heat shrink tubing.

Use either crimp caps or solder to connect the wires. Use shrink tubing if soldering. Optionally, you can use under-hood wiring loom from the auto parts store like I did, to dress up the harness:

They looked like this when I was done:

The harness was installed like this: