To my knowledge there is no legal way to do unlicensed carrier current transmission. Do you have information otherwise? I've always wanted to try it..

The Part15 regulations for AM and FM are more subtle then what you present here. On FM it is based on field strength readings, the exact values of which escape me, but yielding roughly the range you describe.

For AM the rules are more interesting. You can have up to a 3m antenna length and 100mW of DC power input to the final stage of amplification. The optimal setup is a class E amplifier with ~95-99% efficiency into a properly grounded 3m base loaded vertical antenna. The antenna will be grossly undersized but you try to compensate with a huge loading coil. In ideal conditions this setup can get you about 0.5km range.

LPFM is a much more significant undertaking and it is not trivial to get an LPFM license. I know because I have one :)