About the only thing I didn't connect is the "Power Antenna" lead (I don't have a power antenna - that is, the motorized kind).

This is probably the reason you're getting bad reception. Many cars require power to an antenna amplifier. The power antenna lead is designed for this purpose. It also can control a power antenna which is motorized.

You can also use the blue amplifier remote wire from the main sled to power either of those things.

It is important for you to know which wire is the one on your vehicle which powers the antenna amplifier. You might have to do some research to find this wire.

I believe it is (and it's hooked up).

Hooked up TO WHAT?